This notebook contains all multivariate analyses of zoobenthic community structure using the new, nearly unheard-of modeling methods: packages mvabund, boral.
Again, to make it self-contained, there will be the same repetitive setup/data import/preparation part.


Setup!

Define the working subdirectories.

## print the working directory, just to be on the safe side
paste("You are here: ", getwd())

data.dir <- "data"    ## input data files
functions.dir <- "R"  ## functions & scripts
save.dir <- "output"  ## clean data, output from models & more complex calculations
figures.dir <- "figs" ## plots & figures 

Import libraries.

library(here) ## painless relative paths to subdurectories, etc.
library(tidyverse) ## data manipulation, cleaning, aggregation
library(viridis) ## smart & pretty colour schemes
library(mvabund) ## multivariate modeling analyses in ecology
library(boral) ## more multivariate modeling analyses in ecology

Organize some commonly-used ggplot2 modifications into a more convenient (and less repetitive) format. One day, I MUST figure out the proper way to set the theme..

## ggplot settings & things that I keep reusing
# ggplot_theme <- list(
#   theme_bw(),
#   theme(element_text(family = "Times"))
# )

## always use black-and-white theme
theme_set(theme_bw())

## helper to adjust ggplot text size & avoid repetitions 
text_size <- function(text.x = NULL,
                      text.y = NULL,
                      title.x = NULL,
                      title.y = NULL,
                      legend.text = NULL,
                      legend.title = NULL, 
                      strip.x = NULL, 
                      strip.y = NULL) {
  theme(axis.text.x = element_text(size = text.x),
        axis.text.y = element_text(size = text.y),
        axis.title.x = element_text(size = title.x),
        axis.title.y = element_text(size = title.y),
        legend.text = element_text(size = legend.text), 
        legend.title = element_text(size = legend.title), 
        strip.text.x = element_text(size = strip.x), 
        strip.text.y = element_text(size = strip.y)
        )
}


## log y/min + 1 transform - useful for species counts/biomass data visualization
log_y_min <- function(y) {
  log(y / min(y[y > 0]) + 1)
}

Sand stations (Burgas Bay, 2013-2014)

Import zoobenthic abundance data (cleaned and prepared).

zoo.abnd.sand <- read_csv(here(save.dir, "abnd_sand_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.sand <- zoo.abnd.sand %>% 
    mutate(station = factor(station, levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)

Remove the all-0 species (= not present in the current dataset).
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it’s unlikely they carry important information, but it would probably improve the run times).

(zoo.abnd.flt.sand <- zoo.abnd.sand %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
LVM - model-based ordination

Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.
I’m including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of species composition.
NB this takes about a million years to run!

lvm.sand <- boral(y = zoo.abnd.flt.sand, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:6, each = 9), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

Check the summary and diagnostic plots for the LVM.

summary(lvm.sand)
$call
boral.default(y = zoo.abnd.flt.sand, family = "negative.binomial", 
    lv.control = list(num.lv = 2), row.eff = "fixed", row.ids = matrix(rep(1:6, 
        each = 9), ncol = 1))

$coefficients
                             coefficients
cols                           beta0 theta1 theta2 Dispersion
  Abra alba                    3.034  2.067  0.000      1.371
  Abra sp.                    -2.005  2.771  0.816     15.556
  Acanthocardia tuberculata   -2.274  1.260 -1.562     16.177
  Acari                       -0.388 -4.022  2.084      0.570
  Actiniaria                  -2.488  1.690 -1.807     15.660
  Alitta succinea              1.381 -0.236  1.809      2.791
  Ampelisca diadema            4.493  0.352  0.584      1.326
  Amphibalanus improvisus      2.068  0.713  0.703      0.450
  Amphipoda                   -1.105 -2.650 -2.465     21.674
  Amphitritides gracilis      -1.791 -3.324  1.154     16.964
  Ampithoe sp.                -0.281 -0.133 -3.283     18.773
  Anadara kagoshimensis        0.859  1.852  4.266      0.238
  Aonides paucibranchiata      0.472  0.089  4.550      7.285
  Apseudopsis ostroumovi       1.057 -0.277  1.452      8.630
  Aricidea claudiae           -1.715  2.146  2.761     15.827
  Bathyporeia guilliamsoniana  1.511 -1.650 -3.995      0.487
  Bittium reticulatum          4.102  0.729  1.052      1.681
  Bodotria arenosa             1.850 -1.936  0.433      1.662
  Brachynotus sexdentatus     -1.809  2.451  3.065      3.237
  Brachystomia scalaris       -2.397  2.357 -2.053     17.373
  Branchiostoma lanceolatum    2.743 -3.117 -2.628      0.065
  Caecum armoricum            -1.101 -4.421  1.179      2.711
  Caecum trachea              -0.776 -3.904 -0.857      5.222
  Capitella capitata           2.179  0.665  0.576      1.930
  Capitella minima             3.930  1.166  0.855      1.705
  Cardiidae                   -2.447  1.478 -1.967     15.260
  Cerastoderma edule          -1.743  1.899 -1.971     15.710
  Cerastoderma glaucum        -1.999  0.969  1.751     15.707
  Chamelea gallina             5.633  1.721 -2.317      1.106
  Chondrochelia savignyi      -2.056 -2.526  1.229     19.047
  Crassicorophium crassicorne -1.505 -2.188 -2.274     19.588
  Cumopsis goodsir            -2.253  1.461 -1.423     14.973
  Cytharella costulata         0.069  2.060  2.058      0.406
  Decapoda larvae              1.118 -0.073  2.579     18.605
  Dinophilus gyrociliatus      0.409 -1.987  2.337      1.057
  Diogenes pugilator           2.558  0.499  0.168      0.183
  Donax venustus              -1.159  2.382 -3.044      1.242
  Elaphognathia bacescoi      -2.404 -2.059  0.440     16.337
  Eteone flava                -1.942  1.799 -1.850     10.773
  Eteone sp.                   1.828 -0.743  0.204      4.988
  Eulalia viridis             -0.987 -1.251  2.564     14.003
  Eunice vittata              -0.804 -2.901  3.628      0.831
  Eurydice dollfusi            3.146 -3.292 -2.101      3.104
  Eurydice pontica            -2.073 -1.745 -1.221     15.862
  Exogone naidina              3.637 -0.275  0.023      2.696
  Gammaridae                  -0.360 -1.693 -3.027     17.631
  Gastrosaccus sanctus         0.949 -0.144 -1.788      7.116
  Genetyllis tuberculata       2.478 -0.784 -0.332      6.841
  Glycera sp.                 -0.330 -0.469  3.700      8.451
  Glycera tridactyla           1.570  3.176  1.300      1.166
  Harmothoe imbricata         -1.542  2.992  2.753     18.237
  Harmothoe reticulata         0.900 -0.196  3.914      0.333
  Heteromastus filiformis      2.442  2.526  4.885      0.043
  Hirudinea                    1.354 -3.600 -0.802      0.175
  Holothuroidea               -2.328 -3.734  1.699      2.841
  Hydrobia acuta              -2.218  1.657  1.640     15.278
  Hydrobia sp.                -0.608 -0.750 -0.812     15.252
  Iphinoe sp.                 -2.134 -1.589 -1.154     14.630
  Iphinoe tenella             -0.202  1.669  4.353      0.896
  Kellia suborbicularis       -0.761  1.982  3.458      7.811
  Lagis koreni                 1.323  1.323  3.547      0.140
  Leiochone leiopygos          0.317  1.044  3.558      0.857
  Lentidium mediterraneum     -1.885  4.346 -5.874      1.711
  Leptosynapta inhaerens      -2.061 -3.529  1.869     12.925
  Lindrilus flavocapitatus     2.032 -3.402 -0.227     18.202
  Loripes orbiculatus         -0.107  3.385 -1.775      2.631
  Lucinella divaricata        -1.390  4.183 -2.954      4.244
  Lysidice ninetta            -2.027 -1.584 -1.092     15.360
  Mactra stultorum            -2.102  1.957 -1.975     11.329
  Magelona papillicornis       0.267  1.099 -3.028      0.508
  Magelona rosea              -1.424  1.780 -1.995      8.537
  Maldanidae                  -2.301  1.343 -1.418     16.293
  Melinna palmata              0.963  4.703  5.149      0.390
  Melita palmata              -2.567 -5.922  4.219      0.397
  Microdeutopus gryllotalpa    0.457  0.771 -0.131     13.748
  Microdeutopus sp.           -2.395  1.413 -1.483     16.132
  Microdeutopus versiculatus  -2.138 -6.456  6.071      0.180
  Micromaldane ornithochaeta  -1.493  2.356 -2.870      2.582
  Micronephthys stammeri       4.042  0.742  0.335      0.668
  Microphthalmus fragilis      0.182 -4.746 -2.826      3.756
  Microphthalmus sp.           1.791 -1.206 -1.430     18.404
  Monocorophium acherusicum    3.075 -0.086  2.262      0.959
  Monocorophium insidiosum    -1.554  2.045 -2.129     16.095
  Mysta picta                  1.559  0.048 -0.928      2.602
  Mytilaster lineatus          2.511  0.341  0.431      0.375
  Mytilus galloprovincialis   -1.399 -2.240  2.540     18.634
  Neanthes sp.                -2.171  0.248  1.999     15.514
  Nemertea                     4.175 -0.238 -0.139      2.209
  Nephtyidae                  -1.752  1.801 -1.734     17.817
  Nephtys cirrosa              2.215  2.488 -0.330      0.849
  Nereididae                  -2.113 -1.536 -1.540     16.028
  Nereis pelagica             -2.074 -2.851  1.598     19.917
  Nereis perivisceralis       -2.219 -3.375  2.016      6.490
  Nereis pulsatoria           -0.997  2.766  1.103     11.809
  Nototropis guttatus          2.955 -1.176 -1.006      0.345
  Odostomia plicata            0.247  2.593 -0.752      9.063
  Oligochaeta                  5.959 -2.072  1.615      2.151
  Ophelia limacina             1.312 -3.643 -3.635      0.369
  Papillicardium papillosum   -2.499  2.090 -2.433      9.902
  Paradoneis harpagonea       -1.489  2.514 -2.175      6.434
  Parthenina interstincta     -0.607  2.147 -0.713      6.571
  Parvicardium exiguum         3.072  1.298  1.150      0.216
  Perinereis cultrifera        1.889 -1.533 -0.786      4.739
  Perioculodes longimanus      3.089  0.650  0.435      1.270
  Pestarella candida          -2.589 -1.900  1.142     13.771
  Pholoe inornata             -1.993 -3.032  1.875     17.339
  Phoronida                   -0.933  3.835  2.050      0.843
  Phyllodoce sp.               0.844 -1.005  0.181      9.481
  Pisces larvae               -2.280  1.542  1.820     15.897
  Pisione remota               0.069 -1.778 -0.553      2.985
  Pitar rudis                 -0.341 -0.672  4.606      3.726
  Platyhelminthes             -1.347 -3.187 -0.562      1.415
  Platynereis dumerilii       -2.122 -3.034  1.585     16.516
  Polititapes aureus          -1.528  1.018  2.902      9.056
  Polychaeta larvae           -1.436 -2.389 -1.916     15.664
  Polycirrus caliendrum       -1.841 -5.293  2.686      5.841
  Polycirrus jubatus          -2.499 -5.348  3.715      0.234
  Polydora ciliata             0.653  4.206  3.235      1.400
  Polygordius neapolitanus     2.846 -2.825  0.967      1.906
  Prionospio cirrifera         4.239  0.787  2.204      3.383
  Protodorvillea kefersteini   5.860 -2.421  0.373      1.877
  Protodrilus sp.             -1.334 -2.490 -2.389     20.465
  Pseudocuma longicorne        2.155  0.156 -3.806      0.539
  Rapana venosa               -2.158  2.839  3.278      3.104
  Retusa truncatula           -2.476  1.344 -2.005     15.705
  Retusa variabilis           -1.700  1.365 -2.537      9.018
  Rhithropanopeus harrisii    -2.535 -1.886  1.110     15.951
  Rissoa membranacea          -1.602  2.084 -3.277     14.842
  Sabellaria taurica          -2.013  2.920  2.987      3.203
  Salvatoria clavata          -0.858 -4.189  0.104      4.844
  Schistomeringos rudolphi    -0.186 -2.449  1.168      1.258
  Sphaerosyllis hystrix        3.130 -1.380  0.694      1.571
  Spio filicornis              1.221  2.722 -3.594      8.274
  Spionidae                    0.814 -0.774  2.134     21.195
  Spisula subtruncata          0.761  2.431 -2.127      0.367
  Stenothoe monoculoides      -2.484 -1.864  1.054     15.901
  Sternaspis scutata          -1.195 -2.659 -1.758     21.126
  Steromphala divaricata      -2.275 -2.980  1.828      7.680
  Streptosyllis bidentata     -2.426 -5.506  3.088      0.168
  Syllis gracilis             -0.059 -1.454  3.630      0.812
  Syllis hyalina              -2.660 -4.623  2.517      0.699
  Tellina fabula              -1.597  2.134 -2.042     15.961
  Tellina tenuis               2.349  1.404 -0.872      2.226
  Tritia neritea              -1.986  2.641 -4.137      0.924
  Tritia reticulata            1.263 -0.353  0.755      7.614
  Turbellaria                  2.672  0.138  0.413      2.855
  Upogebia pusilla            -2.482 -1.866  1.117     14.601

$lvs
    lv
rows    lv1    lv2
  1   0.641  0.648
  2   0.659  0.712
  3   0.586  0.729
  4   0.521  0.717
  5   0.614  0.622
  6   0.537  0.574
  7   0.681  0.657
  8   0.615  0.744
  9   0.543  0.805
  10  0.085  0.640
  11  0.078  0.759
  12  0.116  0.716
  13  0.266  0.563
  14  0.102  0.592
  15  0.187  0.450
  16  0.242  0.649
  17  0.009  0.835
  18  0.324  0.662
  19 -0.714 -0.346
  20 -0.776 -0.314
  21 -0.738 -0.277
  22 -0.700 -0.306
  23 -0.587 -0.328
  24 -0.517 -0.298
  25 -0.520 -0.446
  26 -0.673 -0.463
  27 -0.464 -0.479
  28  0.497 -0.732
  29  0.454 -0.855
  30  0.699 -0.845
  31  0.478 -0.705
  32  0.515 -0.645
  33  0.408 -0.713
  34  0.893 -0.979
  35  0.846 -1.088
  36  1.037 -0.890
  37 -1.123  0.538
  38 -1.150  0.456
  39 -1.066  0.537
  40 -1.114  0.406
  41 -1.091  0.399
  42 -1.068  0.407
  43 -1.201  0.342
  44 -1.157  0.513
  45 -1.098  0.589
  46  0.903 -0.746
  47  0.860 -0.744
  48  0.786 -0.753
  49  0.481 -0.592
  50  0.660 -0.701
  51  0.622 -0.710
  52  0.786 -0.680
  53  0.761 -0.712
  54  0.733 -0.799

$row.coefficients
$row.coefficients[[1]]
     1      2      3      4      5      6 
-3.069 -2.875 -2.636 -3.750 -2.854 -3.010 


$est
[1] "median"

$calc.ics
[1] FALSE

$trial.size
  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 [43] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 [85] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[127] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

$num.ord.levels
[1] 0

$prior.control
$prior.control$ssvs.index
[1] -1


attr(,"class")
[1] "summary.boral"
## model fit diagnostic plots
plot(lvm.sand)
NULL

The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a normal distribution of the residuals) - the model fits the data pretty well.

Save the sand LVM.

write_rds(lvm.sand, 
          here(save.dir, "lvm_sand.RDS"))

Save the diagnostic plots.

png(here(figures.dir, "diagnostic_lvm_sand.png"), width = 25, height = 20, units = "cm", res = 300)
par(mfrow = c(2, 2))
plot(lvm.sand)
NULL
par(mfrow = c(1, 1))
dev.off()
null device 
          1 

Examine the biplot obtained by fitting the LVM, as well as the 20 most “important” species.

lvsplot(lvm.sand, jitter = T, biplot = TRUE, ind.spp = 20)
Only the first 20 ``most important'' latent variable coefficients included in biplot

All in all, the final result resembles the nMDS ordination very much - same 4 clusters (Kraimorie + Chukalya, AKin, Agalina, Sozopol + Paraskeva). Kraimorie and Chukalya are better distinguished on the LVM plot than on the MDS, but still.
The run time is extremely, extremely long (~1h), but the data don’t need to be transformed, and the model fit can be examined and adjusted if necessary.
The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I’m not adding the species on top, first because I’m too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.

Make the plot and save it.

(plot.lvm.sand <- ggplot(lvs.coord.sand) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("S", as.numeric((unique(lvs.coord.sand %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

## save the LVM plot for the sand stations
ggsave(file = here(figures.dir, "lvm_sand.png"), 
       plot.lvm.sand, 
       width = 15, units = "cm", dpi = 300)
GLM fitting for abundance - environmental data

Let’s fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.
These functions all come from package mvabund.
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (2009-2011 + 2013-2014) at each station, repeated for each replicate, and the sediment data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.

env.sand <- read_csv(here(save.dir, "env_data_ordinations_sand.csv"))

## convert station to factor
(env.sand <- env.sand %>% 
    mutate(station = factor(station,
                            levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)

Station is a factor, the rest of the variables are numeric.

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.

## there is already one subset of filtered count data (54 x 147) - use it 
zoo.mvabnd.sand <- mvabund(zoo.abnd.flt.sand)
manyGLM by LVM clusters

First, let’s see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.

## construct the vector of the clusters by hand, it's easier that way.. 
lvm.clusters.sand <- c(rep(1, times = 18), rep(2:4, each = 9), rep(3, times = 9))

## convert to factor
(lvm.clusters.sand <- factor(lvm.clusters.sand))

Check the model assumptions. 1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.
Another way: direct plotting (variance ~ mean), for each species within each factor level.

plot(manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.sand ~ lvm.clusters.sand, table = TRUE)
START SECTION 2 
Plotting if overlay is TRUE
using grouping variable lvm.clusters.sand 290 mean values were 0 and could 
                                        not be included in the log-plot
using grouping variable lvm.clusters.sand 290 variance values were 0 and could not 
                                        be included in the log-plot
FINISHED SECTION 2 
$mean
  Chamelea.gallina Protodorvillea.kefersteini Oligochaeta Microdeutopus.versiculatus
1        5.0555556                 22.7222222  29.2222222                  0.1666667
2       10.1111111                190.5555556 187.0000000                  0.0000000
3      140.3888889                  0.8333333   0.2222222                  0.0000000
4        0.3333333                 60.2222222  20.2222222                136.5555556
  Heteromastus.filiformis Melinna.palmata Prionospio.cirrifera Lentidium.mediterraneum
1             62.72222222     51.55555556           26.0000000                 0.00000
2              0.00000000      0.00000000            3.0000000                 0.00000
3              0.05555556      0.05555556            0.3333333                21.77778
4              0.22222222      0.00000000            0.0000000                 0.00000
  Eurydice.dollfusi Polygordius.neapolitanus Branchiostoma.lanceolatum Ampelisca.diadema
1         0.0000000                 1.333333                 0.0000000          9.944444
2         6.5555556                 8.444444                23.1111111          6.666667
3         0.7777778                 0.000000                 0.5555556          2.111111
4        34.7777778                22.888889                 9.5555556          1.333333
  Melita.palmata Bittium.reticulatum Capitella.minima Nemertea Micronephthys.stammeri
1        0.00000           9.7222222        6.4444444 2.222222               3.944444
2        0.00000           3.8888889        0.1111111 3.555556               0.000000
3        0.00000           1.0555556        2.6666667 2.055556               3.277778
4       31.77778           0.8888889        2.1111111 6.666667               3.222222
  Pseudocuma.longicorne Polycirrus.caliendrum Sphaerosyllis.hystrix
1             0.0000000               0.00000             1.0000000
2             3.3333333               0.00000             2.7777778
3             7.0000000               0.00000             0.2222222
4             0.1111111              17.22222            11.1111111
  Monocorophium.acherusicum Polycirrus.jubatus Ophelia.limacina Spio.filicornis
1                 4.9444444            0.00000        0.0000000      0.05555556
2                 0.7777778            0.00000       12.3333333      0.00000000
3                 0.1111111            0.00000        0.1111111      7.11111111
4                 5.3333333           14.88889        2.2222222      0.00000000
   Hirudinea Lindrilus.flavocapitatus Polydora.ciliata Streptosyllis.bidentata
1 0.05555556                0.2222222        6.7222222                 0.00000
2 4.11111111               13.6666667        0.0000000                 0.00000
3 0.00000000                0.0000000        0.1111111                 0.00000
4 9.88888889                0.0000000        0.0000000                13.66667
        Acari Anadara.kagoshimensis Abra.alba Parvicardium.exiguum Exogone.naidina
1  0.05555556              5.666667 3.0000000            4.0000000       1.2777778
2  0.33333333              0.000000 0.4444444            0.3333333       0.6666667
3  0.00000000              0.000000 2.3888889            0.9444444       1.2222222
4 11.88888889              0.000000 0.0000000            0.5555556       4.5555556
  Nototropis.guttatus Microphthalmus.fragilis Lagis.koreni Nephtys.cirrosa
1           0.4444444                0.000000    4.2222222       1.0000000
2           4.7777778                6.333333    0.1111111       0.0000000
3           0.6111111                0.000000    0.0000000       3.1111111
4           2.3333333                2.777778    0.2222222       0.2222222
  Lucinella.divaricata Perioculodes.longimanus Bathyporeia.guilliamsoniana
1             0.000000               2.1666667                   0.0000000
2             0.000000               1.3333333                   4.7777778
3             3.666667               0.5555556                   1.1111111
4             0.000000               0.5555556                   0.1111111
  Glycera.tridactyla Tellina.tenuis Aonides.paucibranchiata Caecum.armoricum
1          2.7222222      0.5000000               2.8333333        0.0000000
2          0.0000000      0.5555556               0.0000000        0.2222222
3          0.7777778      2.3333333               0.0000000        0.0000000
4          0.1111111      0.0000000               0.4444444        5.7777778
  Bodotria.arenosa Spisula.subtruncata Harmothoe.reticulata Eunice.vittata Turbellaria
1        0.3333333          0.05555556             1.888889      0.1666667   1.1111111
2        1.4444444          0.00000000             0.000000      0.0000000   0.4444444
3        0.0000000          2.72222222             0.000000      0.0000000   0.3888889
4        3.5555556          0.00000000             1.555556      4.4444444   1.0000000
  Diogenes.pugilator Loripes.orbiculatus Mytilaster.lineatus Genetyllis.tuberculata
1          0.9444444          0.05555556           1.0555556              0.1111111
2          0.7777778          0.00000000           1.0000000              0.0000000
3          0.5555556          2.00000000           0.3333333              0.5000000
4          0.4444444          0.00000000           0.3333333              2.7777778
  Iphinoe.tenella Dinophilus.gyrociliatus Perinereis.cultrifera Pitar.rudis
1        1.888889              0.27777778            0.05555556   1.2222222
2        0.000000              0.00000000            0.33333333   0.0000000
3        0.000000              0.05555556            0.27777778   0.0000000
4        0.000000              3.00000000            2.33333333   0.7777778
  Syllis.hyalina Leiochone.leiopygos Salvatoria.clavata Amphibalanus.improvisus
1       0.000000           1.4444444          0.0000000               0.9444444
2       0.000000           0.0000000          0.5555556               0.4444444
3       0.000000           0.0000000          0.0000000               0.2222222
4       3.222222           0.2222222          2.5555556               0.2222222
  Capitella.capitata Syllis.gracilis Decapoda.larvae Magelona.papillicornis
1          0.7777778       0.3888889       1.2777778              0.0000000
2          0.2222222       0.0000000       0.1111111              0.1111111
3          0.3888889       0.0000000       0.0000000              1.2222222
4          0.4444444       2.1111111       0.1111111              0.0000000
  Tritia.neritea Alitta.succinea Eteone.sp. Schistomeringos.rudolphi Microphthalmus.sp.
1       0.000000      0.50000000  0.2222222               0.00000000          0.0000000
2       0.000000      0.11111111  0.0000000               0.00000000          0.0000000
3       1.222222      0.05555556  0.2222222               0.05555556          0.3888889
4       0.000000      1.11111111  1.4444444               1.88888889          1.0000000
  Caecum.trachea Donax.venustus Mysta.picta Glycera.sp. Odostomia.plicata
1      0.0000000      0.0000000   0.1111111   0.6111111         0.1111111
2      0.5555556      0.0000000   0.2222222   0.0000000         0.0000000
3      0.0000000      0.8333333   0.4444444   0.0000000         0.6111111
4      1.1111111      0.0000000   0.3333333   0.3333333         0.0000000
  Apseudopsis.ostroumovi Cytharella.costulata Kellia.suborbicularis
1             0.38888889           0.61111111             0.6666667
2             0.00000000           0.00000000             0.0000000
3             0.05555556           0.05555556             0.0000000
4             0.44444444           0.00000000             0.0000000
  Leptosynapta.inhaerens Spionidae Tritia.reticulata Gastrosaccus.sanctus
1               0.000000 0.3888889         0.3888889           0.05555556
2               0.000000 0.1111111         0.5555556           0.66666667
3               0.000000 0.0000000         0.0000000           0.22222222
4               1.333333 0.4444444         0.0000000           0.00000000
  Micromaldane.ornithochaeta  Phoronida Holothuroidea Nereis.perivisceralis
1                  0.0000000 0.55555556      0.000000                     0
2                  0.0000000 0.00000000      0.000000                     0
3                  0.6111111 0.05555556      0.000000                     0
4                  0.0000000 0.00000000      1.111111                     1
  Phyllodoce.sp. Amphitritides.gracilis Gammaridae Amphipoda Harmothoe.imbricata
1     0.11111111              0.0000000 0.00000000 0.0000000           0.3888889
2     0.22222222              0.0000000 0.77777778 0.7777778           0.0000000
3     0.05555556              0.0000000 0.05555556 0.0000000           0.0000000
4     0.44444444              0.8888889 0.00000000 0.0000000           0.0000000
  Mytilus.galloprovincialis Pholoe.inornata Pisione.remota Ampithoe.sp.
1                0.05555556       0.0000000     0.05555556    0.0000000
2                0.00000000       0.0000000     0.44444444    0.3333333
3                0.00000000       0.0000000     0.00000000    0.1666667
4                0.66666667       0.7777778     0.22222222    0.0000000
  Paradoneis.harpagonea Platyhelminthes Platynereis.dumerilii Rissoa.membranacea
1             0.0000000       0.0000000             0.0000000          0.0000000
2             0.0000000       0.2222222             0.0000000          0.0000000
3             0.3333333       0.0000000             0.0000000          0.3333333
4             0.0000000       0.4444444             0.6666667          0.0000000
  Brachynotus.sexdentatus Eulalia.viridis Microdeutopus.gryllotalpa Nereis.pelagica
1               0.2777778      0.05555556                 0.1111111       0.0000000
2               0.0000000      0.00000000                 0.1111111       0.0000000
3               0.0000000      0.00000000                 0.1111111       0.0000000
4               0.0000000      0.44444444                 0.0000000       0.5555556
  Rapana.venosa Sabellaria.taurica Steromphala.divaricata Aricidea.claudiae
1     0.2777778          0.2777778              0.0000000         0.2222222
2     0.0000000          0.0000000              0.0000000         0.0000000
3     0.0000000          0.0000000              0.0000000         0.0000000
4     0.0000000          0.0000000              0.5555556         0.0000000
  Monocorophium.insidiosum Nereis.pulsatoria Parthenina.interstincta Protodrilus.sp.
1                0.0000000        0.16666667              0.05555556       0.0000000
2                0.0000000        0.00000000              0.00000000       0.4444444
3                0.2222222        0.05555556              0.16666667       0.0000000
4                0.0000000        0.00000000              0.00000000       0.0000000
  Sternaspis.scutata Tellina.fabula Cerastoderma.edule Chondrochelia.savignyi
1          0.0000000      0.0000000          0.0000000              0.0000000
2          0.4444444      0.0000000          0.0000000              0.0000000
3          0.0000000      0.2222222          0.1666667              0.0000000
4          0.0000000      0.0000000          0.0000000              0.3333333
  Crassicorophium.crassicorne Magelona.rosea Polititapes.aureus Polychaeta.larvae
1                   0.0000000      0.0000000          0.1666667         0.0000000
2                   0.3333333      0.0000000          0.0000000         0.3333333
3                   0.0000000      0.1666667          0.0000000         0.0000000
4                   0.0000000      0.0000000          0.0000000         0.0000000
  Retusa.variabilis Brachystomia.scalaris Eteone.flava Hydrobia.sp. Mactra.stultorum
1         0.0000000             0.0000000    0.0000000   0.00000000        0.0000000
2         0.0000000             0.0000000    0.0000000   0.00000000        0.0000000
3         0.1666667             0.1111111    0.1111111   0.05555556        0.1111111
4         0.0000000             0.0000000    0.0000000   0.11111111        0.0000000
  Nephtyidae Papillicardium.papillosum   Abra.sp. Acanthocardia.tuberculata Actiniaria
1  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
2  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
3  0.1111111                 0.1111111 0.05555556                0.05555556 0.05555556
4  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
   Cardiidae Cerastoderma.glaucum Cumopsis.goodsir Elaphognathia.bacescoi
1 0.00000000           0.05555556       0.00000000              0.0000000
2 0.00000000           0.00000000       0.00000000              0.0000000
3 0.05555556           0.00000000       0.05555556              0.0000000
4 0.00000000           0.00000000       0.00000000              0.1111111
  Eurydice.pontica Hydrobia.acuta Iphinoe.sp. Lysidice.ninetta Maldanidae
1        0.0000000     0.05555556   0.0000000        0.0000000 0.00000000
2        0.1111111     0.00000000   0.1111111        0.1111111 0.00000000
3        0.0000000     0.00000000   0.0000000        0.0000000 0.05555556
4        0.0000000     0.00000000   0.0000000        0.0000000 0.00000000
  Microdeutopus.sp. Neanthes.sp. Nereididae Pestarella.candida Pisces.larvae
1        0.00000000   0.05555556  0.0000000          0.0000000    0.05555556
2        0.00000000   0.00000000  0.1111111          0.0000000    0.00000000
3        0.05555556   0.00000000  0.0000000          0.0000000    0.00000000
4        0.00000000   0.00000000  0.0000000          0.1111111    0.00000000
  Retusa.truncatula Rhithropanopeus.harrisii Stenothoe.monoculoides Upogebia.pusilla
1        0.00000000                0.0000000              0.0000000        0.0000000
2        0.00000000                0.0000000              0.0000000        0.0000000
3        0.05555556                0.0000000              0.0000000        0.0000000
4        0.00000000                0.1111111              0.1111111        0.1111111

$var
  Chamelea.gallina Protodorvillea.kefersteini  Oligochaeta Microdeutopus.versiculatus
1         32.05556                707.0359477 3.339477e+02                      0.500
2         38.86111               7209.2777778 3.244850e+04                      0.000
3       7120.36928                  0.9705882 3.006536e-01                      0.000
4          0.25000               2202.9444444 1.089444e+02                   8235.778
  Heteromastus.filiformis Melinna.palmata Prionospio.cirrifera Lentidium.mediterraneum
1            1.564683e+03    2.225908e+03          339.2941176                   0.000
2            0.000000e+00    0.000000e+00           17.7500000                   0.000
3            5.555556e-02    5.555556e-02            0.4705882                2097.242
4            4.444444e-01    0.000000e+00            0.0000000                   0.000
  Eurydice.dollfusi Polygordius.neapolitanus Branchiostoma.lanceolatum Ampelisca.diadema
1          0.000000                 10.23529                 0.0000000         107.93791
2         46.277778                 50.02778                52.8611111          59.50000
3          3.712418                  0.00000                 0.7320261           7.51634
4        638.944444                 68.11111                12.0277778           1.50000
  Melita.palmata Bittium.reticulatum Capitella.minima  Nemertea Micronephthys.stammeri
1         0.0000          142.447712       48.2614379  4.418301              12.173203
2         0.0000            9.861111        0.1111111 45.777778               0.000000
3         0.0000            1.349673       38.0000000  9.702614               5.388889
4       281.4444            1.611111        5.3611111 62.750000               3.944444
  Pseudocuma.longicorne Polycirrus.caliendrum Sphaerosyllis.hystrix
1             0.0000000                0.0000             2.7058824
2            16.0000000                0.0000             8.9444444
3            38.0000000                0.0000             0.5359477
4             0.1111111              323.6944            72.8611111
  Monocorophium.acherusicum Polycirrus.jubatus Ophelia.limacina Spio.filicornis
1                17.7026144            0.00000        0.0000000      0.05555556
2                 1.4444444            0.00000       42.5000000      0.00000000
3                 0.1045752            0.00000        0.1045752    136.81045752
4                26.0000000           64.11111        6.1944444      0.00000000
    Hirudinea Lindrilus.flavocapitatus Polydora.ciliata Streptosyllis.bidentata
1  0.05555556                0.8888889       64.5653595                    0.00
2  8.11111111              338.2500000        0.0000000                    0.00
3  0.00000000                0.0000000        0.1045752                    0.00
4 36.61111111                0.0000000        0.0000000                   18.75
        Acari Anadara.kagoshimensis Abra.alba Parvicardium.exiguum Exogone.naidina
1  0.05555556              10.23529 10.470588            7.0588235        1.506536
2  0.50000000               0.00000  1.777778            0.2500000        0.750000
3  0.00000000               0.00000  6.604575            1.2320261        1.947712
4 69.61111111               0.00000  0.000000            0.5277778       59.277778
  Nototropis.guttatus Microphthalmus.fragilis Lagis.koreni Nephtys.cirrosa
1           0.3790850                 0.00000    7.3594771       3.2941176
2           8.1944444                33.50000    0.1111111       0.0000000
3           0.8398693                 0.00000    0.0000000       6.4575163
4           5.2500000                13.94444    0.1944444       0.4444444
  Lucinella.divaricata Perioculodes.longimanus Bathyporeia.guilliamsoniana
1              0.00000               2.8529412                   0.0000000
2              0.00000               3.2500000                   6.9444444
3             56.23529               0.7320261                   1.7516340
4              0.00000               1.7777778                   0.1111111
  Glycera.tridactyla Tellina.tenuis Aonides.paucibranchiata Caecum.armoricum
1         14.0947712      0.5000000               18.852941        0.0000000
2          0.0000000      0.5277778                0.000000        0.4444444
3          1.8300654     16.5882353                0.000000        0.0000000
4          0.1111111      0.0000000                1.027778       55.9444444
  Bodotria.arenosa Spisula.subtruncata Harmothoe.reticulata Eunice.vittata Turbellaria
1        0.7058824          0.05555556             2.928105      0.1470588   4.3398693
2        5.2777778          0.00000000             0.000000      0.0000000   0.5277778
3        0.0000000          6.44771242             0.000000      0.0000000   0.7222222
4        4.5277778          0.00000000             1.277778     13.5277778   1.2500000
  Diogenes.pugilator Loripes.orbiculatus Mytilaster.lineatus Genetyllis.tuberculata
1          0.7614379          0.05555556           0.7614379              0.1045752
2          1.1944444          0.00000000           2.0000000              0.0000000
3          0.3790850          9.05882353           0.2352941              0.8529412
4          0.2777778          0.00000000           0.2500000             15.1944444
  Iphinoe.tenella Dinophilus.gyrociliatus Perinereis.cultrifera Pitar.rudis
1         3.51634              0.56535948            0.05555556    8.771242
2         0.00000              0.00000000            1.00000000    0.000000
3         0.00000              0.05555556            0.21241830    0.000000
4         0.00000              5.75000000            7.50000000    1.194444
  Syllis.hyalina Leiochone.leiopygos Salvatoria.clavata Amphibalanus.improvisus
1       0.000000           2.0261438          0.0000000               0.8790850
2       0.000000           0.0000000          0.7777778               0.5277778
3       0.000000           0.0000000          0.0000000               0.1830065
4       8.444444           0.4444444         11.5277778               0.1944444
  Capitella.capitata Syllis.gracilis Decapoda.larvae Magelona.papillicornis
1          1.5947712       0.4869281      14.8006536              0.0000000
2          0.4444444       0.0000000       0.1111111              0.1111111
3          0.3692810       0.0000000       0.0000000              0.8888889
4          0.7777778       2.8611111       0.1111111              0.0000000
  Tritia.neritea Alitta.succinea Eteone.sp. Schistomeringos.rudolphi Microphthalmus.sp.
1       0.000000      0.85294118  0.3006536               0.00000000          0.0000000
2       0.000000      0.11111111  0.0000000               0.00000000          0.0000000
3       3.477124      0.05555556  0.3006536               0.05555556          0.7222222
4       0.000000      1.61111111  3.5277778               2.11111111          4.5000000
  Caecum.trachea Donax.venustus Mysta.picta Glycera.sp. Odostomia.plicata
1       0.000000       0.000000   0.1045752    1.663399         0.2222222
2       1.777778       0.000000   0.1944444    0.000000         0.0000000
3       0.000000       1.088235   0.6143791    0.000000         1.6633987
4       2.861111       0.000000   0.5000000    0.500000         0.0000000
  Apseudopsis.ostroumovi Cytharella.costulata Kellia.suborbicularis
1             0.60457516           0.36928105              1.882353
2             0.00000000           0.00000000              0.000000
3             0.05555556           0.05555556              0.000000
4             1.02777778           0.00000000              0.000000
  Leptosynapta.inhaerens Spionidae Tritia.reticulata Gastrosaccus.sanctus
1                   0.00 2.7222222          0.369281           0.05555556
2                   0.00 0.1111111          1.777778           1.25000000
3                   0.00 0.0000000          0.000000           0.30065359
4                   8.75 1.0277778          0.000000           0.00000000
  Micromaldane.ornithochaeta  Phoronida Holothuroidea Nereis.perivisceralis
1                   0.000000 0.73202614      0.000000                  0.00
2                   0.000000 0.00000000      0.000000                  0.00
3                   1.075163 0.05555556      0.000000                  0.00
4                   0.000000 0.00000000      1.861111                  2.75
  Phyllodoce.sp. Amphitritides.gracilis Gammaridae Amphipoda Harmothoe.imbricata
1     0.10457516               0.000000 0.00000000  0.000000             2.01634
2     0.44444444               0.000000 2.94444444  5.444444             0.00000
3     0.05555556               0.000000 0.05555556  0.000000             0.00000
4     0.77777778               4.111111 0.00000000  0.000000             0.00000
  Mytilus.galloprovincialis Pholoe.inornata Pisione.remota Ampithoe.sp.
1                0.05555556        0.000000     0.05555556    0.0000000
2                0.00000000        0.000000     0.52777778    1.0000000
3                0.00000000        0.000000     0.00000000    0.2647059
4                4.00000000        3.944444     0.19444444    0.0000000
  Paradoneis.harpagonea Platyhelminthes Platynereis.dumerilii Rissoa.membranacea
1             0.0000000       0.0000000                  0.00          0.0000000
2             0.0000000       0.1944444                  0.00          0.0000000
3             0.5882353       0.0000000                  0.00          0.9411765
4             0.0000000       0.2777778                  2.75          0.0000000
  Brachynotus.sexdentatus Eulalia.viridis Microdeutopus.gryllotalpa Nereis.pelagica
1               0.3300654      0.05555556                 0.2222222        0.000000
2               0.0000000      0.00000000                 0.1111111        0.000000
3               0.0000000      0.00000000                 0.1045752        0.000000
4               0.0000000      1.02777778                 0.0000000        2.777778
  Rapana.venosa Sabellaria.taurica Steromphala.divaricata Aricidea.claudiae
1     0.3300654          0.3300654              0.0000000         0.5359477
2     0.0000000          0.0000000              0.0000000         0.0000000
3     0.0000000          0.0000000              0.0000000         0.0000000
4     0.0000000          0.0000000              0.7777778         0.0000000
  Monocorophium.insidiosum Nereis.pulsatoria Parthenina.interstincta Protodrilus.sp.
1                0.0000000        0.26470588              0.05555556        0.000000
2                0.0000000        0.00000000              0.00000000        1.777778
3                0.5359477        0.05555556              0.14705882        0.000000
4                0.0000000        0.00000000              0.00000000        0.000000
  Sternaspis.scutata Tellina.fabula Cerastoderma.edule Chondrochelia.savignyi
1           0.000000      0.0000000          0.0000000                      0
2           1.777778      0.0000000          0.0000000                      0
3           0.000000      0.4183007          0.2647059                      0
4           0.000000      0.0000000          0.0000000                      1
  Crassicorophium.crassicorne Magelona.rosea Polititapes.aureus Polychaeta.larvae
1                           0      0.0000000          0.1470588               0.0
2                           1      0.0000000          0.0000000               0.5
3                           0      0.1470588          0.0000000               0.0
4                           0      0.0000000          0.0000000               0.0
  Retusa.variabilis Brachystomia.scalaris Eteone.flava Hydrobia.sp. Mactra.stultorum
1         0.0000000             0.0000000    0.0000000   0.00000000        0.0000000
2         0.0000000             0.0000000    0.0000000   0.00000000        0.0000000
3         0.1470588             0.2222222    0.1045752   0.05555556        0.1045752
4         0.0000000             0.0000000    0.0000000   0.11111111        0.0000000
  Nephtyidae Papillicardium.papillosum   Abra.sp. Acanthocardia.tuberculata Actiniaria
1  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
2  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
3  0.2222222                 0.1045752 0.05555556                0.05555556 0.05555556
4  0.0000000                 0.0000000 0.00000000                0.00000000 0.00000000
   Cardiidae Cerastoderma.glaucum Cumopsis.goodsir Elaphognathia.bacescoi
1 0.00000000           0.05555556       0.00000000              0.0000000
2 0.00000000           0.00000000       0.00000000              0.0000000
3 0.05555556           0.00000000       0.05555556              0.0000000
4 0.00000000           0.00000000       0.00000000              0.1111111
  Eurydice.pontica Hydrobia.acuta Iphinoe.sp. Lysidice.ninetta Maldanidae
1        0.0000000     0.05555556   0.0000000        0.0000000 0.00000000
2        0.1111111     0.00000000   0.1111111        0.1111111 0.00000000
3        0.0000000     0.00000000   0.0000000        0.0000000 0.05555556
4        0.0000000     0.00000000   0.0000000        0.0000000 0.00000000
  Microdeutopus.sp. Neanthes.sp. Nereididae Pestarella.candida Pisces.larvae
1        0.00000000   0.05555556  0.0000000          0.0000000    0.05555556
2        0.00000000   0.00000000  0.1111111          0.0000000    0.00000000
3        0.05555556   0.00000000  0.0000000          0.0000000    0.00000000
4        0.00000000   0.00000000  0.0000000          0.1111111    0.00000000
  Retusa.truncatula Rhithropanopeus.harrisii Stenothoe.monoculoides Upogebia.pusilla
1        0.00000000                0.0000000              0.0000000        0.0000000
2        0.00000000                0.0000000              0.0000000        0.0000000
3        0.05555556                0.0000000              0.0000000        0.0000000
4        0.00000000                0.1111111              0.1111111        0.1111111

It’s not perfect, but it’s not too terrible either.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula. When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.

Everything looks more or less fine; fit the model.

glms.lvm.sand <- manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, 
                         family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

I really don’t like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.
Update (2019/05/02): while I still think these are fugly, I have no more time or nerves to deal with it. Rainbow shit it is.

png(here(figures.dir, "diagnostic_glms_lvm_sand.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(glms.lvm.sand, which = 1:3)
dev.off()
null device 
          1 

Save the model!

write_rds(glms.lvm.sand, 
          here(save.dir, "glms_lvm_sand.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.sand.summary <- summary(glms.lvm.sand, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)

The factor (here - groups outlined by the LVM) is highly significant according to the models.
This also allows us to see which species exhibit a response to the chosen factor. The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. I’ll save the summary for safekeeping, but I’ll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).

write_rds(glms.lvm.sand.summary, 
          here(save.dir, "glms_lvm_sand_summary.RDS"))

Run the anova on the model.

(glms.lvm.sand.aov <- anova.manyglm(glms.lvm.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)

I probably shouldn’t have printed all this out, but oh well who cares.

Save the ANOVA, too.

write_rds(glms.lvm.sand.aov, 
          here(save.dir, "glms_lvm_sand_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern (here - clusters in the LVM, which are really the different soft-bottom habitats).

top_n_sp_glm <- function(glms.aov, tot.dev.expl = 0.75) {
  ## helper retrieving the top n species with the highest contribution to the patterns tested by the GLMs, in decreasing order.
  ## Arguments: glms.aov - results from an ANOVA on the fitted GLMs
  ##            dev.explained - proportion of explained deviance to use as cutoff
  
  ## get the change in deviance due to the tested pattern (= 2nd row from table of univariate test stats), and sort the species in order of decreasing contribution
  uni.sorted <- sort(glms.aov$uni.test[2, ], decreasing = TRUE, index.return = FALSE)

  ## start at 10 species and check how much of the deviance is explained by their contributions. Repeat, increasing by increments of 10 until the desired explained deviance (set at function call) is reached. 
  top.n.sp <- 10
  dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  
  while(dev.expl < tot.dev.expl) {
    top.n.sp <- top.n.sp + 10
    dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  }
  
  ## print the total deviance explained - just for information
  print(paste("Total deviance explained:", round(dev.expl, 3)))
  
  ## return the final top species (and their univariate contributions, just in case) 
  top.sp <- uni.sorted[1:top.n.sp]
  return(top.sp)
}

## get the top contributing species for the initial sand GLMs 
(top.sp.glms.lvm.sand <- top_n_sp_glm(glms.lvm.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.sand) <- names(top.sp.glms.lvm.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.sand

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.lvm.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.sand))))
)

plot_top_n <- function(top.n.sp.data, mapping, labs.legend, lab.y, palette) {
  ## helper for plotting top n species. Was hoping to avoid repeating it from way back when, but no dice. 
  ## Arguments: top.n.sp.data - data frame (long) of top species' counts/biomasses at the different stations
  ##            mapping - mappings of the aesthetics
  ##            labs.legend - labels the use for the legend entries
  ##            lab.y - custom label for y axis
  ##            palette - custom colour palette (for consistency with other plots)
  
  ggplot(top.n.sp.data, mapping) +
    geom_point(alpha = 0.75) + # make points larger & partially transparent
    scale_color_brewer(palette = palette,  labels = labs.legend) + 
    ylab(lab.y) + 
    coord_flip() 
}


(plot.top.sp.glms.lvm.sand <- plot_top_n(abnd.top.sp.glms.lvm.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("S", as.numeric(unique(abnd.top.sp.glms.lvm.sand$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)

Well this is a nightmarish plot.. I’ll probably just put this awfulness in a table and call it a day, or play with lvsplot and the modeled ordination plot, if a plot is what’s needed.

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is hopelessly ugly and clumsy (and I’ll have to repeat it for the seagrass, too!), but I’m tired of being stuck on this. I still have many, MANY more things to do, and more time-consuming ones too..

top_sp_glms_table <- function(manyglms.obj.smry, group, p = 0.05) {
  ### extracts the top species in a group for which there is an observed effect in a manyglm test, at the specified probability level.
  ### Returns: tibble with the top species for the specified group/cluster, sorted (descending) by univariate LR value of the species, significant at the given p level. 
  
  ## extract the univariate LR coefficients of the species and their p-values 
  sp_univar <- as_tibble(manyglms.obj.smry$uni.test, rownames = "species")
  sp_p <- as_tibble(manyglms.obj.smry$uni.p, rownames = "species")

  ## combine in the same tibble
  sp_all <- left_join(sp_univar, sp_p, by = "species")  
  
  ## rename the columns
  sp_all <- sp_all %>% 
    rename_at(vars(contains(".x")), list(~str_replace_all(., pattern = ".x", ".LR"))) %>% 
    rename_at(vars(contains(".y")), list(~str_replace_all(., pattern = ".y", ".p")))
  
  ## filter only the group/cluster we want, at the p-level we want
  sp_all_flt <- sp_all %>% 
    select(species, contains(group)) %>% 
    filter_at(vars(contains(".p")), all_vars(. < p)) %>%
    arrange_at(vars(contains(".LR")), list(~desc(.)))

}

top.sp.abnd.glms.lvm.sand <- lapply(names(glms.lvm.sand.summary$aliased), function(x) top_sp_glms_table(glms.lvm.sand.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.sand2" etc.
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("lvm.clusters.sand")), list(~str_replace_all(., pattern = "lvm.clusters.sand", "group_"))))

top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.sand.long <- zoo.abnd.sand %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))

## sum sp abundances by group; nest by group
zoo.abnd.sand.long.smry <- zoo.abnd.sand.long %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, zoo.abnd.sand.long.smry %>% pull(group), ~left_join(.x, zoo.abnd.sand.long.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, c(18, 9, 18, 9), function(x, y) x %>% mutate(mean_count = total_count/y))
)

To determine the relative taxon contribution to patterns: LR statistic - a measure of strength of individual taxon contributions. LR expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or, compared to a critical value, to decide whether to reject the null model in favour of the alternative model.

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.
For group 1 (= S1-S2), the species/taxa with significantly higher abundance are: Oligochaeta, H. filiformis, P. kefersteini, M. palmata, P. cirrifera, A. diadema (among others); and the ones with significantly lower abundance - even 0, in some cases - S. bidentata, B.lanceolatum, M. papillicornis, Melita palmata, P. jubatus, and so on.
For group 2 (= S3), the species with higher abundance are: B. lanceolatum, O. limacina, Oligochaeta (this is this strange artifact of 2013), P. kefersteini, L. flavocapitatus. The species with lower abundance are: H. filiformis, A. kagoshimensis, M. stammeri, Melinna palmata, etc. For group 3 (= S4-S6), the species with higher abundance are: C. gallina, L. mediterraneum - with very high dominance over practically all others; also Pseudocuma longicorne, Spio filicornis. The species with lower abundance are: H. filiformis, Oligochaetes (to a certain extent - they are still present, though), A. kagoshimensis, L. koreni, Harmothoe reticulata, Iphinoe tenella, Leiochone leiopygos.
For group 4 (= S5), the species with higher abundance are: Microdeutopus versiculatus, Eurydice dollfusi, Melita palmata, Polygordius neapolitanus, Polycirrus caliendrum, Polycirrus jubatus, Streptosyllis bidentata. The species with lower abundance are: A. kagoshimensis, Melinna palmata, P. cirrifera, P. ciliata, A. alba, I. tenella.
I love how the species with the highest variances (e.g. C. gallina, the most conspicuous example) are consistently pushed back - have lower LR scores. This is very good - C. gallina in particular is dominant in group 3, but is present also in all other groups - its substrate/depth preferences are very wide, so this is not uncommon. It’s not automatically pushed to the top of the list, but its reaction is detected by the manyGLM test. Neat! Contrast to the SIMPER results, where the species with the highest variance are consistently at the top - they contribute the most to the similarity, as per the test definition.

I’m going to save these as separate files (manually), then format them as tables - I know it’s a shame, but I’m too frustrated to figure out how to do it programmatically.
I’ll also put them in a word table in my final text, because I don’t want to deal with a million separate ones (embedded excel tables don’t split over multiple pages).

NB In my text, I’m switching the names/places of group 3 and 4, to be consistent with the SIMPER groups (I’m NOT going to repeat all this just to have the numbers match up). So the file names, table names, etc. remain as above. But in the text, I’ll have the following: group 1 = S1-S2, group 2 = S3, group 3 = S5, group 4 = S4-S6. REMEMBER THIS SO THERE IS NO CONFUSION!

manyGLM by environmental parameters

Now, let’s try to see a different thing - which environmental parameters best describe the species response.
I’m going to use the PCA-filtered environmental data - it’s still going to be a slog, with 7 potential predictors..
First, construct the formula for the model - will do it separately in case I need to update it later, etc. This is the full formula with all explanatory variables.

(formula.env.glms.sand <- formula(paste("zoo.mvabnd.sand ~", 
                                        paste(env.sand %>% select(-station) %>% names(), collapse = "+")))
)

Fit the GLMs to the sand abundance data.

env.glms.sand <- manyglm(formula.env.glms.sand,
                         data = env.sand,
                         family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(env.glms.sand)


## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.sand, which = 1:3)


# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

Well, it’s good enough if you ask me (still the kinda strange “line” at lin.pred = -6; otherwise residuals are random enough).

Save the model!

write_rds(env.glms.sand, 
          here(save.dir, "glms_env_sand.RDS"))

Before anything else, I want to try and reduce the model a little - to improve the fit/reduce run time.
The automatic step functions that eliminate/add model terms sequentially don’t work - they fail at the last step with a cryptic error about differing numbers of rows - I assume because manyglm has as left side term the whole community abundance matrix, and the functions don’t really know how to deal with that. I don’t understand enough about their internals to fix the problem, so I’m just going to write my own little automation based on the function drop1.

evaluate_glms_env <- function(full.mod) {
  ### sequentially eliminate model terms in manyglms vs environmental parameters, and find the best model based on lowest AIC score.
  ### Arguments: full.mod - full model fit
  ### Returns: best manyglm model of environmental parameters; prints out the best model formula
  ### Dependencies: tidyverse   
  

  ## get the starting formula (= full model with all variables)
  start.formula <- formula(full.mod)

  drop_var <- function(mod) {
    ### helper picking the next variable to drop from a model to improve the fit (based on AIC)
    
    ## check the model AICs if variables are dropped one by one
    drop1.df <- as_tibble(drop1(mod), rownames = "drop_var") %>% arrange(AIC)
    
    ## pick the variable to drop next - the one resulting in the largest decrease in AIC
    drop.var <- drop1.df %>% filter(AIC == min(AIC)) %>% pull(drop_var)
    return(drop.var)
  }
  
  ## pick the variable to drop next
  drop.var <- drop_var(full.mod)

  if(drop.var != "<none>") {
     ## update the model formula, dropping the variable resulting in the largest decrease in AIC; then apply it to the model.
    new.formula <- update.formula(start.formula, paste0("~. -", drop.var))
    new.mod <- update(full.mod, new.formula)

    ## identify a new variable to drop that lowers the AIC
    drop.var <- drop_var(new.mod)
    
    ## repeat the steps above until the function can no longer find such a variable (i.e., dropping more variables doesn't improve the model fit)
    while(drop.var != "<none>") {
      new.formula <- update.formula(new.formula, paste0("~. -", drop.var))
      new.mod <- update(full.mod, new.formula)
      drop.var <- drop_var(new.mod)
    }
    
    ## print out the best model formula
    print(paste("Best model: ", paste(deparse(new.formula), collapse = "")))
    return(new.mod)
    
  } else {
    ## if the starting model is the best, print its formula (fat chance!)
    print(paste("Best model: ", paste(deparse(start.formula), collapse = "")))
    return(full.mod)
  }
  
}

Select the best reduced model of environmental variables for the sand stations.

## selection function defined in the sand section 
top.env.glm.red.sand <- evaluate_glms_env(env.glms.sand)

Check its fit.

## residuals vs fitted values
plot(top.env.glm.red.sand)

## all traditional (g)lm diagnostic plots
plot.manyglm(top.env.glm.red.sand, which = 1:3)

I think it’s fine; might even be better than the full model.. Save it, too.

write_rds(top.env.glm.red.sand, 
          here(save.dir, "glms_top_env_red_sand.RDS"))

Save the model diagnostic plots.

png(here(figures.dir, "diagnostic_top_glm_env_red_sand.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(top.env.glm.red.sand, which = 1:3)
dev.off()
null device 
          1 

Run ANOVA on this model.

(top.env.glm.red.sand.aov <- anova.manyglm(top.env.glm.red.sand,
                                           test = "LR", p.uni = "adjusted",
                                           nBoot = 999, ## limit the number of permutations for a shorter run time   
                                           show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.01 minutes...
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Time elapsed: 0 hr 16 min 18 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.sand ~ PO4 + seston + LUSI + gravel, 
Model:     family = "negative.binomial", data = env.sand)

Multivariate test:
            Res.Df Df.diff    Dev Pr(>Dev)    
(Intercept)     53                            
PO4             52       1 1147.2    0.001 ***
seston          51       1  816.4    0.001 ***
LUSI            50       1  728.5    0.001 ***
gravel          49       1 1128.7    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
            Abra.alba          Abra.sp.          Acanthocardia.tuberculata         
                  Dev Pr(>Dev)      Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                        
PO4             1.011    1.000    0.513    1.000                     3.576    0.979
             Acari          Actiniaria          Alitta.succinea         
               Dev Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                             
PO4         10.498    0.120      0.513    1.000           0.065    1.000
            Ampelisca.diadema          Amphibalanus.improvisus          Amphipoda
                          Dev Pr(>Dev)                     Dev Pr(>Dev)       Dev
(Intercept)                                                                      
PO4                    12.592    0.032                  11.462    0.081     0.552
                     Amphitritides.gracilis          Ampithoe.sp.         
            Pr(>Dev)                    Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                               
PO4            1.000                  2.571    1.000        0.032    1.000
            Anadara.kagoshimensis          Aonides.paucibranchiata         
                              Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                
PO4                        67.791    0.001                   5.965    0.659
            Apseudopsis.ostroumovi          Aricidea.claudiae         
                               Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                           
PO4                          0.375    1.000             7.633    0.402
            Bathyporeia.guilliamsoniana          Bittium.reticulatum         
                                    Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                  
PO4                               0.002    1.000              22.784    0.002
            Bodotria.arenosa          Brachynotus.sexdentatus         
                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                           
PO4                      1.3    1.000                  11.298    0.085
            Brachystomia.scalaris          Branchiostoma.lanceolatum         
                              Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                  
PO4                         0.696    1.000                     0.057    1.000
            Caecum.armoricum          Caecum.trachea          Capitella.capitata
                         Dev Pr(>Dev)            Dev Pr(>Dev)                Dev
(Intercept)                                                                     
PO4                    7.463    0.427          1.119    1.000              1.193
                     Capitella.minima          Cardiidae          Cerastoderma.edule
            Pr(>Dev)              Dev Pr(>Dev)       Dev Pr(>Dev)                Dev
(Intercept)                                                                         
PO4            1.000             2.53    1.000     0.513    1.000              7.708
                     Cerastoderma.glaucum          Chamelea.gallina         
            Pr(>Dev)                  Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                 
PO4            0.384                1.415    1.000           27.316    0.001
            Chondrochelia.savignyi          Crassicorophium.crassicorne         
                               Dev Pr(>Dev)                         Dev Pr(>Dev)
(Intercept)                                                                     
PO4                          1.246    1.000                       0.459    1.000
            Cumopsis.goodsir          Cytharella.costulata          Decapoda.larvae
                         Dev Pr(>Dev)                  Dev Pr(>Dev)             Dev
(Intercept)                                                                        
PO4                    3.576    0.969               16.556    0.008           4.389
                     Dinophilus.gyrociliatus          Diogenes.pugilator         
            Pr(>Dev)                     Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
PO4            0.845                   3.462    0.988              2.328    1.000
            Donax.venustus          Elaphognathia.bacescoi          Eteone.flava
                       Dev Pr(>Dev)                    Dev Pr(>Dev)          Dev
(Intercept)                                                                     
PO4                 11.663    0.069                  1.021    1.000        7.158
                     Eteone.sp.          Eulalia.viridis          Eunice.vittata
            Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)            Dev
(Intercept)                                                                     
PO4            0.480      3.247    0.996           0.508    1.000          5.957
                     Eurydice.dollfusi          Eurydice.pontica         
            Pr(>Dev)               Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                              
PO4            0.659             7.553    0.419            0.243    1.000
            Exogone.naidina          Gammaridae          Gastrosaccus.sanctus         
                        Dev Pr(>Dev)        Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
PO4                   1.544    1.000      0.215    1.000                0.001    1.000
            Genetyllis.tuberculata          Glycera.sp.          Glycera.tridactyla
                               Dev Pr(>Dev)         Dev Pr(>Dev)                Dev
(Intercept)                                                                        
PO4                          9.748    0.149       1.819    1.000              4.038
                     Harmothoe.imbricata          Harmothoe.reticulata         
            Pr(>Dev)                 Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                    
PO4            0.882               7.572    0.416                6.871    0.582
            Heteromastus.filiformis          Hirudinea          Holothuroidea         
                                Dev Pr(>Dev)       Dev Pr(>Dev)           Dev Pr(>Dev)
(Intercept)                                                                           
PO4                          55.658    0.001     4.073    0.876         6.327    0.634
            Hydrobia.acuta          Hydrobia.sp.          Iphinoe.sp.         
                       Dev Pr(>Dev)          Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                                   
PO4                  3.566    0.988        3.379    0.993       0.243    1.000
            Iphinoe.tenella          Kellia.suborbicularis          Lagis.koreni
                        Dev Pr(>Dev)                   Dev Pr(>Dev)          Dev
(Intercept)                                                                     
PO4                  38.241    0.001                12.137    0.052       48.067
                     Leiochone.leiopygos          Lentidium.mediterraneum         
            Pr(>Dev)                 Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                       
PO4            0.001              20.554    0.003                  16.232    0.009
            Leptosynapta.inhaerens          Lindrilus.flavocapitatus         
                               Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                  
PO4                          3.875    0.905                    4.746    0.795
            Loripes.orbiculatus          Lucinella.divaricata          Lysidice.ninetta
                            Dev Pr(>Dev)                  Dev Pr(>Dev)              Dev
(Intercept)                                                                            
PO4                      14.871    0.012               19.259    0.004            0.243
                     Mactra.stultorum          Magelona.papillicornis         
            Pr(>Dev)              Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                   
PO4            1.000            2.401    1.000                 19.059    0.004
            Magelona.rosea          Maldanidae          Melinna.palmata         
                       Dev Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                     
PO4                   4.77    0.795      3.576    0.979          75.355    0.001
            Melita.palmata          Microdeutopus.gryllotalpa          Microdeutopus.sp.
                       Dev Pr(>Dev)                       Dev Pr(>Dev)               Dev
(Intercept)                                                                             
PO4                 14.255    0.019                     0.001    1.000             3.576
                     Microdeutopus.versiculatus          Micromaldane.ornithochaeta
            Pr(>Dev)                        Dev Pr(>Dev)                        Dev
(Intercept)                                                                        
PO4            0.971                       9.28    0.172                     10.809
                     Micronephthys.stammeri          Microphthalmus.fragilis         
            Pr(>Dev)                    Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
PO4            0.098                  0.016    1.000                   0.028    1.000
            Microphthalmus.sp.          Monocorophium.acherusicum         
                           Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                               
PO4                      8.692    0.220                     3.627    0.966
            Monocorophium.insidiosum          Mysta.picta          Mytilaster.lineatus
                                 Dev Pr(>Dev)         Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
PO4                            7.646    0.401       4.088    0.876               9.876
                     Mytilus.galloprovincialis          Neanthes.sp.          Nemertea
            Pr(>Dev)                       Dev Pr(>Dev)          Dev Pr(>Dev)      Dev
(Intercept)                                                                           
PO4            0.143                     0.507    1.000        1.415    1.000    0.718
                     Nephtyidae          Nephtys.cirrosa          Nereididae         
            Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                          
PO4            1.000      3.733    0.931           3.455    0.989      0.243    1.000
            Nereis.pelagica          Nereis.perivisceralis          Nereis.pulsatoria
                        Dev Pr(>Dev)                   Dev Pr(>Dev)               Dev
(Intercept)                                                                          
PO4                   1.278    1.000                 5.021    0.764              1.04
                     Nototropis.guttatus          Odostomia.plicata          Oligochaeta
            Pr(>Dev)                 Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                             
PO4            1.000               0.017    1.000             2.158    1.000      12.804
                     Ophelia.limacina          Papillicardium.papillosum         
            Pr(>Dev)              Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)     <NA>             <NA>     <NA>                      <NA>     <NA>
PO4            0.032             1.13    1.000                     1.026    1.000
            Paradoneis.harpagonea          Parthenina.interstincta         
                              Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                  <NA>     <NA>                    <NA>     <NA>
PO4                        16.021    0.009                   0.628    1.000
            Parvicardium.exiguum          Perinereis.cultrifera         
                             Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                 <NA>     <NA>                  <NA>     <NA>
PO4                        14.43    0.013                 6.906    0.582
            Perioculodes.longimanus          Pestarella.candida          Pholoe.inornata
                                Dev Pr(>Dev)                Dev Pr(>Dev)             Dev
(Intercept)                    <NA>     <NA>               <NA>     <NA>            <NA>
PO4                          13.283    0.026              1.021    1.000           2.532
                     Phoronida          Phyllodoce.sp.          Pisces.larvae         
            Pr(>Dev)       Dev Pr(>Dev)            Dev Pr(>Dev)           Dev Pr(>Dev)
(Intercept)     <NA>      <NA>     <NA>           <NA>     <NA>          <NA>     <NA>
PO4            1.000    14.128    0.020          0.214    1.000         3.566    0.979
            Pisione.remota          Pitar.rudis          Platyhelminthes         
                       Dev Pr(>Dev)         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)           <NA>     <NA>        <NA>     <NA>            <NA>     <NA>
PO4                  0.184    1.000        2.33    1.000           1.258    1.000
            Platynereis.dumerilii          Polititapes.aureus          Polychaeta.larvae
                              Dev Pr(>Dev)                Dev Pr(>Dev)               Dev
(Intercept)                  <NA>     <NA>               <NA>     <NA>              <NA>
PO4                          2.51    1.000              5.232    0.758             0.667
                     Polycirrus.caliendrum          Polycirrus.jubatus         
            Pr(>Dev)                   Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)     <NA>                  <NA>     <NA>               <NA>     <NA>
PO4            1.000                 8.778    0.213             14.046    0.021
            Polydora.ciliata          Polygordius.neapolitanus         
                         Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)             <NA>     <NA>                     <NA>     <NA>
PO4                    33.47    0.001                    1.738    1.000
            Prionospio.cirrifera          Protodorvillea.kefersteini         
                             Dev Pr(>Dev)                        Dev Pr(>Dev)
(Intercept)                 <NA>     <NA>                       <NA>     <NA>
PO4                       48.371    0.001                      2.268    1.000
            Protodrilus.sp.          Pseudocuma.longicorne          Rapana.venosa
                        Dev Pr(>Dev)                   Dev Pr(>Dev)           Dev
(Intercept)            <NA>     <NA>                  <NA>     <NA>          <NA>
PO4                   0.497    1.000                13.533    0.024        16.327
                     Retusa.truncatula          Retusa.variabilis         
            Pr(>Dev)               Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)     <NA>              <NA>     <NA>              <NA>     <NA>
PO4            0.008             0.513    1.000              4.77    0.795
            Rhithropanopeus.harrisii          Rissoa.membranacea         
                                 Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                     <NA>     <NA>               <NA>     <NA>
PO4                            1.021    1.000              2.111    1.000
            Sabellaria.taurica          Salvatoria.clavata         
                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)               <NA>     <NA>               <NA>     <NA>
PO4                     16.327    0.008              2.946    0.999
            Schistomeringos.rudolphi          Sphaerosyllis.hystrix         
                                 Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                     <NA>     <NA>                  <NA>     <NA>
PO4                           11.176    0.087                 3.042    0.998
            Spio.filicornis          Spionidae          Spisula.subtruncata         
                        Dev Pr(>Dev)       Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)            <NA>     <NA>      <NA>     <NA>                <NA>     <NA>
PO4                   8.141    0.262     0.278    1.000              34.272    0.001
            Stenothoe.monoculoides          Sternaspis.scutata         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                   <NA>     <NA>               <NA>     <NA>
PO4                          1.021    1.000              0.497    1.000
            Steromphala.divaricata          Streptosyllis.bidentata         
                               Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                   <NA>     <NA>                    <NA>     <NA>
PO4                           3.62    0.966                  14.133    0.020
            Syllis.gracilis          Syllis.hyalina          Tellina.fabula         
                        Dev Pr(>Dev)            Dev Pr(>Dev)            Dev Pr(>Dev)
(Intercept)            <NA>     <NA>           <NA>     <NA>           <NA>     <NA>
PO4                   1.059    1.000         11.199    0.086          7.846    0.291
            Tellina.tenuis          Tritia.neritea          Tritia.reticulata         
                       Dev Pr(>Dev)            Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)           <NA>     <NA>           <NA>     <NA>              <NA>     <NA>
PO4                  5.219    0.758          9.738    0.149             7.578    0.416
            Turbellaria          Upogebia.pusilla         
                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)        <NA>     <NA>             <NA>     <NA>
PO4               0.973    1.000            1.021    1.000
 [ reached getOption("max.print") -- omitted 3 rows ]
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

So, it turns out that the long-term water column eutrophication (PO4, seston), the anthropogenic pressure in general (LUSI), and the sediment composition (gravel) explain the observed community patterns best.

Save the ANOVA - I really, really don’t want to have to repeat it.

write_rds(top.env.glm.red.sand.aov, 
          here(save.dir, "glms_top_env_red_sand_anova.RDS"))

Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).

## get the top contributing species for the environmental parameter sand GLMs 
(top.sp.glms.env.red.sand <- top_n_sp_glm(top.env.glm.red.sand.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.817"
           Melinna.palmata      Anadara.kagoshimensis    Heteromastus.filiformis 
                 75.354817                  67.790515                  55.657621 
      Prionospio.cirrifera               Lagis.koreni            Iphinoe.tenella 
                 48.371413                  48.067236                  38.240757 
       Spisula.subtruncata           Polydora.ciliata           Chamelea.gallina 
                 34.272034                  33.469990                  27.316472 
       Bittium.reticulatum        Leiochone.leiopygos       Lucinella.divaricata 
                 22.783736                  20.553990                  19.259453 
    Magelona.papillicornis       Cytharella.costulata         Sabellaria.taurica 
                 19.059044                  16.556175                  16.326603 
             Rapana.venosa    Lentidium.mediterraneum      Paradoneis.harpagonea 
                 16.326603                  16.231882                  16.021000 
       Loripes.orbiculatus       Parvicardium.exiguum             Melita.palmata 
                 14.870959                  14.429942                  14.255372 
   Streptosyllis.bidentata                  Phoronida         Polycirrus.jubatus 
                 14.133303                  14.128398                  14.045827 
     Pseudocuma.longicorne    Perioculodes.longimanus                Oligochaeta 
                 13.533423                  13.282665                  12.804148 
         Ampelisca.diadema      Kellia.suborbicularis             Donax.venustus 
                 12.591581                  12.137452                  11.662509 
   Amphibalanus.improvisus    Brachynotus.sexdentatus             Syllis.hyalina 
                 11.462125                  11.298400                  11.198693 
  Schistomeringos.rudolphi Micromaldane.ornithochaeta                      Acari 
                 11.176121                  10.809322                  10.498478 
       Mytilaster.lineatus     Genetyllis.tuberculata             Tritia.neritea 
                  9.875996                   9.747742                   9.737885 
Microdeutopus.versiculatus      Polycirrus.caliendrum         Microphthalmus.sp. 
                  9.280497                   8.778395                   8.692123 
           Spio.filicornis             Tellina.fabula         Cerastoderma.edule 
                  8.140655                   7.845543                   7.707880 
  Monocorophium.insidiosum          Aricidea.claudiae          Tritia.reticulata 
                  7.646026                   7.632964                   7.577649 
       Harmothoe.imbricata          Eurydice.dollfusi 
                  7.571700                   7.553233 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   DON'T BE IN A HURRY TO DO THAT IF YOU WANT TO SUBSET THE ORIGINAL MATRIX BEFORE RUNNING TRAITGLM 
names(top.sp.glms.env.red.sand) <- names(top.sp.glms.env.red.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

I’m going to plot these top contributing species, but I’m not using the plot. At least this time it’s more manageable, but still not presentable enough..

## get the species and their abundances from the original count data, and transform them to long format
abnd.top.sp.glms.env.red.sand <- zoo.abnd.sand %>% 
  select(station, names(top.sp.glms.env.red.sand)) %>% 
  gather(key = "species", value = "count", -station) %>% 
  ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
  mutate(species = factor(species, levels = rev(names(top.sp.glms.env.red.sand)))) %>% 
  ## add clusters from LVM as a column
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1,
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))
## add the significant environmental parameters from the model
(abnd.top.sp.glms.env.red.sand <- left_join(abnd.top.sp.glms.env.red.sand, 
                                            env.sand %>% select(station, PO4, seston, LUSI, gravel), 
                                            by = "station") 
    
)
(plot.top.sp.glms.env.red.sand <- plot_top_n(abnd.top.sp.glms.env.red.sand,
                                             mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                             labs.legend = unique(abnd.top.sp.glms.env.red.sand$group),
                                             lab.y = "Abundance (log(y/min + 1))",
                                             palette = "Set2") + 
    theme(legend.position = "top")
)

FIXME>>> Try another thing - manually, unfortunately: this same nightmare, but colored by the values of each model term.

Extract the taxon information (univariate tests) from the model ANOVA to present as a table (probably better than this plot, although it’s informative).

## extract the univariate test coefficients (LR) from the environmental model ANOVA. NB keep the row names when converting the matrix to tibble! 
table.top.sp.glms.env.red.sand <- as_tibble(top.env.glm.red.sand.aov$uni.test, rownames = "var")
## fix the species names - remove first dor  
names(table.top.sp.glms.env.red.sand) <- names(table.top.sp.glms.env.red.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")
## subset only the top species (explaining ~75% of the dataset variation)
table.top.sp.glms.env.red.sand <- table.top.sp.glms.env.red.sand %>% 
  select(var, names(top.sp.glms.env.red.sand))
## transpose, because a table with 50 columns is just unreadable
(table.top.sp.glms.env.red.sand <- table.top.sp.glms.env.red.sand %>%
    gather(key = species, value = value, -var) %>% 
    spread(key = var, value = value) %>% 
    ## arrange as before (terms in the order they appear in the model, and by descending value of the LR for the first model term - here, PO4). Also get rid of the intercept (it's all-NA anyway).
    select(species, PO4, seston, LUSI, gravel) %>%
    arrange(desc(PO4)) 
)

Save this to a file - will have to format it as a nice table by hand, unfortunately.

write_csv(table.top.sp.glms.env.red.sand, 
          here(save.dir, "taxa_contrib_glms_top_env_red_sand.csv"))

Calculate the percentage contribution of each of these species to each of the model terms (Dev(term) = Sum-of-LR - sum of the LRs for the individual univariate species tests)..

## get the total deviance (Sum-of-LR) for each model term
(dev.terms.top.glms.env.sand <- as_tibble(top.env.glm.red.sand.aov$table, rownames = "var") %>%
   ## get rid of unnecessary variables (I only want the deviance value for each term) and intercept term 
   select(var, Dev) %>% 
   filter(var != "(Intercept)") %>% 
   ## transpose 
   gather(variable, value, -var) %>%
   spread(var, value) %>% 
   ## get rid of first column and rearrange columns to match table of deviances of univariate tests for species 
   select(-variable) %>% 
   select(PO4, seston, LUSI, gravel)
)  
## calculate the proportion contribution of each species to each parameter deviance
prop.top.sp.glms.env.red.sand <- map2_df(table.top.sp.glms.env.red.sand %>% select(-species),
                                         dev.terms.top.glms.env.sand, 
                                         ~.x/.y)
## add back the species 
(prop.top.sp.glms.env.red.sand <- bind_cols(table.top.sp.glms.env.red.sand %>% select(species), 
                                            prop.top.sp.glms.env.red.sand)
)

Final analysis to try: which species respond differently to different environmental parameters? (= traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix).
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.

sp.response.glms.env.red.sand <- traitglm(L = mvabund(zoo.abnd.flt.sand[, names(top.sp.glms.env.red.sand)]), 
                                          R = as.matrix(env.sand %>% select(PO4, seston, LUSI, gravel)), 
                                          method = "manyglm")
No traits matrix entered, so will fit SDMs with different env response for each spp 
sp.response.glms.env.red.sand$fourth.corner
                                            PO4      seston          LUSI       gravel
names.L.Ampelisca.diadema             3.9255509  -2.9690187  -0.817892764  -0.54638276
names.L.Amphibalanus.improvisus       4.0226904  -3.2428168  -0.613822194  -0.55947227
names.L.Anadara.kagoshimensis        11.2652127  -7.5624621  -2.881581827  -0.56229429
names.L.Aricidea.claudiae             6.4545107  -6.0030102   0.075837116  -0.81658105
names.L.Bittium.reticulatum           3.6728293  -3.2566010  -0.227682651  -0.60908662
names.L.Brachynotus.sexdentatus      12.2714488  -8.7953746  -2.768356521  -1.15909023
names.L.Cerastoderma.edule           86.3144545 -68.5410436 -16.124587996 -15.76009706
names.L.Chamelea.gallina              4.9735567  -4.0806520  -0.915304631  -0.90870404
names.L.Cytharella.costulata          5.9066074  -4.5531016  -1.156170995  -0.64061054
names.L.Donax.venustus               29.2665146 -25.3133054  -3.196472244  -7.48930781
names.L.Eurydice.dollfusi          -145.3134807  78.0140182  56.500452934  -1.12048695
names.L.Genetyllis.tuberculata        4.9508698  -4.4226734  -0.717237975  -0.50545895
names.L.Harmothoe.imbricata           8.7688494  -8.0381252  -0.174424875  -1.40001396
names.L.Heteromastus.filiformis      16.4489612 -11.8603189  -4.679979720  -0.53453476
names.L.Iphinoe.tenella               9.6429106  -6.3711957  -2.467970830  -0.34728546
names.L.Kellia.suborbicularis        18.1479826 -13.1444944  -4.028384566  -2.38364695
names.L.Lagis.koreni                  5.2752482  -3.9409882  -1.063633817  -0.49005707
names.L.Leiochone.leiopygos           9.4458023  -7.0107877  -2.426883847  -0.49499547
names.L.Lentidium.mediterraneum       2.2184223  -7.7274293   5.119259705  -3.80721597
names.L.Loripes.orbiculatus          11.9138363 -10.5152606  -1.772124177  -1.53849109
names.L.Lucinella.divaricata          4.3089522  -3.8383729  -0.941760570  -0.90040958
names.L.Magelona.papillicornis       -0.8618886  -1.6184538   2.126924166  -1.13824665
names.L.Melinna.palmata              87.5950547 -62.3176332 -28.320862498  -0.53785792
names.L.Melita.palmata               -1.4068078  -1.4310911   2.175555342   0.04534594
names.L.Microdeutopus.versiculatus    4.5619062  -3.3188059  -1.480537959   0.01704370
names.L.Micromaldane.ornithochaeta    2.0293951  -3.6054716   1.146677297  -1.10488159
names.L.Microphthalmus.sp.            2.4219932  -2.3771910  -0.331905804  -0.45014535
names.L.Monocorophium.insidiosum     91.2704372 -72.4819591 -16.997678796 -16.75142841
names.L.Mytilaster.lineatus           3.6452068  -3.0310816  -0.453771212  -0.56603117
names.L.Oligochaeta                   1.1142783  -0.9168759   0.182815777  -0.26804214
names.L.Paradoneis.harpagonea        44.6268239 -34.6189865 -10.110156651  -6.18181742
names.L.Parvicardium.exiguum          5.4679515  -4.2901258  -1.071674867  -0.60043740
names.L.Perioculodes.longimanus       3.8233980  -3.1155895  -0.537523634  -0.55747087
names.L.Phoronida                     4.3674755  -4.1186121  -0.107432136  -0.69239101
names.L.Polycirrus.caliendrum       -14.6362720 -14.5110317  24.537891679  -3.49252794
names.L.Polycirrus.jubatus           -2.4679942  -2.7467481   4.271575754  -0.36118532
names.L.Polydora.ciliata              5.8538836  -4.5251508  -1.054314612  -0.53519651
names.L.Prionospio.cirrifera          4.6312252  -3.5794420  -0.682191827  -0.61411757
names.L.Pseudocuma.longicorne      -184.7247688  94.1777708  77.116820970  -2.87857061
names.L.Rapana.venosa                 6.2536074  -5.8242086   0.109640812  -0.74952507
names.L.Sabellaria.taurica            6.4201209  -5.9779189   0.094454203  -0.79630833
names.L.Schistomeringos.rudolphi      8.9818953  -6.6900990  -3.539271831  -0.05466283
names.L.Spio.filicornis              23.9025062 -18.4529248  -3.775190226  -6.60866099
names.L.Spisula.subtruncata           8.3692147  -6.4982724  -1.857417192  -1.49042998
names.L.Streptosyllis.bidentata      -1.7193139  -2.0772085   3.037260251  -0.16308400
names.L.Syllis.hyalina               -1.4595610  -2.6762110   3.349712166  -0.32574204
names.L.Tellina.fabula               91.2704372 -72.4819591 -16.997678816 -16.75142841
names.L.Tritia.neritea               -3.8087181  -2.4272915   5.454585358  -1.65134985
names.L.Tritia.reticulata             2.6224780  -1.4687956   0.003212383  -0.74189472
# plot this 
a <- max(abs(sp.response.glms.env.red.sand$fourth.corner))
colort <- colorRampPalette(c("blue","white","red")) 
plot.spp <- lattice::levelplot(t(as.matrix(sp.response.glms.env.red.sand$fourth.corner)), xlab = "Environmental Variables",
                     ylab = "Species", col.regions = colort(100), at = seq(-a, a, length = 100),
                     scales = list(x = list(rot = 45)))
print(plot.spp)

When using LASSO (method = “glm1path”), the algorithm fails to converge - I’m not sure how to interpret it.. Maybe because the function tests each individual species:env.parameter interaction (does it really??), and none of them by themselves are sufficient to explain a species’ response. Not to mention the fact that the samples are not really independent (they are replicates at 6 sites, repeated 3 times).
When using method = “manyglm”, the result is the one shown above. It’s still a bitch to interpret - for example, what is the interpretation of an increase in abundance with for ex. high PO4, but low LUSI? Where are these conditions ever met?

In fact, everything points towards the conclusion that a species response is determined by a combination of eutrophication parameters in its environment (water column characteristics), and the composition of the sediments (organic matter and granulometry).

This is actually sort of similar to the PERMANOVA results, in this particular case. However, it’s much more parsimonious.
In the future, I’m leaning more towards the modeling approach - it allows you to check the model fit to one’s real data; also, there are no data reductions due to calculation of distance matrices.

Seagrass stations (Burgas Bay, 2013-2014)

Import zoobenthic abundance data (cleaned and prepared).

zoo.abnd.zostera <- read_csv(here(save.dir, "abnd_zostera_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.zostera <- zoo.abnd.zostera %>% 
    mutate(station = factor(station, levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)

Remove the all-0 species (= not present in the current dataset).
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it’s unlikely they carry important information, but it would probably improve the run times).

(zoo.abnd.flt.zostera <- zoo.abnd.zostera %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
LVM - model-based ordination

Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.
I’m including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of species composition.
NB this takes about a million years to run!

lvm.zostera
$lv.median
    lv
rows         lv1         lv2
  1   0.63309890 -0.25073642
  2   0.71898027 -0.16747807
  3   0.56064687 -0.42687215
  4   0.55163657 -0.12469639
  5   0.30959676  0.41773437
  6   0.24697111  0.44574266
  7   0.32890487  0.50038030
  8   0.40977917  0.26925607
  9   0.34411131 -0.05246175
  10  0.30640639  0.05764798
  11 -0.03303482 -0.31104596
  12  0.33549294  0.06288344
  13 -0.03183279  0.43841255
  14  0.21965019  0.33806513
  15  0.07264994  0.37467055
  16 -0.13875265  0.24543515
  17  0.33939011 -0.80630032
  18  0.40882237 -0.80301467
  19  0.59538891 -1.03245351
  20  0.42986329 -1.04595929
  21 -0.54406129 -0.20080826
  22 -0.39667039  0.00322858
  23 -0.41168940 -0.04570642
  24 -0.25397763  0.02202463
  25 -0.34106053 -0.05910581
  26 -0.43321098  0.06874185
  27 -0.50763931  0.14043786
  28 -0.51347888  0.14183431
  29 -0.47410593 -0.62677135
  30 -0.55540307 -0.63339799
  31 -0.34249913 -0.33267530
  32 -0.47391655 -0.43313634

$lv.mean
    lv
rows         lv1         lv2
  1   0.63973919 -0.26124190
  2   0.72364848 -0.16915308
  3   0.55817571 -0.44430628
  4   0.55870462 -0.13461030
  5   0.32617886  0.42590230
  6   0.26749204  0.45848328
  7   0.35558090  0.51461245
  8   0.41640225  0.26949766
  9   0.34581668 -0.05487866
  10  0.31356211  0.06276810
  11 -0.03221680 -0.30523138
  12  0.34758050  0.05938987
  13 -0.01393408  0.45245190
  14  0.22407775  0.34634591
  15  0.08224484  0.38367041
  16 -0.13343400  0.25869559
  17  0.34340933 -0.83616118
  18  0.41423752 -0.82540763
  19  0.59973842 -1.07749968
  20  0.43460320 -1.10414702
  21 -0.54179579 -0.19510291
  22 -0.39926045  0.01451361
  23 -0.41257931 -0.05011494
  24 -0.25721275  0.03455823
  25 -0.34203064 -0.04757744
  26 -0.43318198  0.08075325
  27 -0.51194024  0.13275752
  28 -0.51837202  0.14297248
  29 -0.47916725 -0.62290666
  30 -0.56334375 -0.63658030
  31 -0.34773465 -0.33506350
  32 -0.47891407 -0.43205665

$lv.iqr
    lv
rows       lv1       lv2
  1  0.3115049 0.3432342
  2  0.2700754 0.3659362
  3  0.2925739 0.3215977
  4  0.2732491 0.3585541
  5  0.2607338 0.3056026
  6  0.2611162 0.2792944
  7  0.2756551 0.2796141
  8  0.2451521 0.3012650
  9  0.2318232 0.2565478
  10 0.2357820 0.2609933
  11 0.2652560 0.2676580
  12 0.2390352 0.2792553
  13 0.2391694 0.2554568
  14 0.2454424 0.2476183
  15 0.2374709 0.2636803
  16 0.2029496 0.2353137
  17 0.4520713 0.3659810
  18 0.4267797 0.3949317
  19 0.5010253 0.4026903
  20 0.5312290 0.3930040
  21 0.2340643 0.2920227
  22 0.2004030 0.2338392
  23 0.2045751 0.2644804
  24 0.1885636 0.2066522
  25 0.1999420 0.2307883
  26 0.2025090 0.2403377
  27 0.1957638 0.2611411
  28 0.2314553 0.2706260
  29 0.2773997 0.2846295
  30 0.2943060 0.3065804
  31 0.2466440 0.2524183
  32 0.2470145 0.2829039

$lv.sd
    lv
rows       lv1       lv2
  1  0.2341917 0.2743629
  2  0.2162751 0.2850905
  3  0.2242427 0.2650938
  4  0.2142396 0.2642869
  5  0.1958259 0.2295734
  6  0.1983309 0.2104188
  7  0.2107166 0.2153038
  8  0.1865497 0.2251835
  9  0.1703594 0.2036468
  10 0.1826565 0.2052637
  11 0.1891908 0.1905564
  12 0.1886136 0.2189078
  13 0.1870533 0.1969266
  14 0.1821220 0.1903206
  15 0.1791703 0.1910769
  16 0.1518936 0.1748393
  17 0.3375928 0.2637745
  18 0.3304306 0.2823427
  19 0.3813969 0.3139455
  20 0.3814063 0.2875726
  21 0.1635995 0.1936426
  22 0.1546703 0.1755459
  23 0.1497812 0.1893369
  24 0.1458645 0.1729330
  25 0.1450000 0.1708971
  26 0.1451275 0.1798791
  27 0.1391878 0.1978126
  28 0.1661801 0.1965980
  29 0.1919833 0.1960416
  30 0.2015131 0.2014474
  31 0.1727551 0.1803966
  32 0.1774746 0.1960130

$lv.coefs.median
                            coefficients
cols                               beta0       theta1       theta2 Dispersion
  Abra alba                   2.19785384  1.988463626  0.000000000  0.8049710
  Abra sp.                   -1.60785043  1.859713408  0.688985905 20.2173666
  Actiniaria                 -2.57492065  1.839207008 -0.432658357 16.3006332
  Alitta succinea             1.28739235  2.962040553 -0.272685187  5.9091138
  Ampelisca diadema           3.91611800  0.202992064 -2.458107574  1.8919712
  Amphibalanus improvisus     1.24302352  2.971930903  0.827067343  1.1337970
  Ampithoe sp.                0.44422404  0.909656274 -1.998454321 10.0143324
  Anadara kagoshimensis      -2.47575780  1.030848599  2.127959386 15.7072938
  Apherusa bispinosa         -2.42777879 -1.186346054  0.306714995 15.8312141
  Apseudopsis ostroumovi      0.52069614 -5.652683931 -2.381105240  2.0290136
  Bittium reticulatum         5.33821195 -2.188296167  2.471152642  0.8462873
  Brachynotus sexdentatus    -1.43275605  0.671639149 -0.198325734 14.8845937
  Capitella capitata          1.07625034 -5.387945211 -0.927957946  1.1697129
  Capitella minima            4.47866745  0.927828377 -2.811702014  0.8264542
  Chamelea gallina           -0.32847134 -3.872079785  0.432330906  0.5314599
  Chironomidae larvae        -2.27627590 -2.524457814 -2.237411662 11.8214047
  Cumella limicola            0.89602581 -4.777192764 -0.003909736  0.4359523
  Cumella pygmaea            -1.92692093 -2.436270797  1.320853343 12.8210486
  Cytharella costulata       -0.06918885 -0.433108439 -0.631817500  1.3645580
  Diogenes pugilator         -0.17702978  0.967901057 -2.015034852  0.4227392
  Eteone flava               -2.88462586  1.638834488 -2.340887944 15.5943644
  Eunice vittata             -0.77938064  1.004839633 -1.600713823 16.3721423
  Eurydice dollfusi          -1.46534113 -2.008583562  0.878631692 15.6259966
  Exogone naidina            -0.46231222  0.723359263 -3.254358766 15.9232624
  Gastrosaccus sanctus       -2.36760458 -1.359591189  0.508017217 16.8261485
  Genetyllis tuberculata      0.29313773  0.004613975  0.259084557 10.3338149
  Glycera sp.                -0.74025745  2.095496915  0.024122863  5.5252360
  Glycera tridactyla         -1.04090148  1.003043530  2.501384290 12.6891993
  Glycera unicornis          -2.42746001  0.848742769  1.843749657 15.8241885
  Harmothoe imbricata        -0.65275195  0.191966135  3.195701629  5.9202590
  Harmothoe reticulata        0.46198922  0.414995827 -0.246837664  0.9583771
  Heteromastus filiformis     3.94477843  0.050460508  0.370152319  0.6248417
  Hirudinea                  -1.13299662  0.182770515  0.720298897 11.0831905
  Hydrobia acuta             -1.41775138  2.777511939 -0.306523317 21.0315014
  Hydrobia sp.               -0.57701622  2.064729591 -0.425678939 18.1683813
  Iphinoe tenella             0.35193649 -0.092973228  0.673030600  6.8589879
  Kellia suborbicularis      -0.36271897 -3.112249152  4.064857708  3.1940592
  Lagis koreni                1.06163168 -0.468884269  3.133340010  0.2783243
  Leiochone leiopygos         0.31832355 -1.763839564  3.210371962  0.4975771
  Lentidium mediterraneum    -2.09709664 -2.122354336  0.080461836 11.6186072
  Lepidochitona cinerea      -2.44289992 -1.417973748  0.272856397 15.5449148
  Loripes orbiculatus         1.92208361 -2.100947705  0.407646541  0.3970641
  Lucinella divaricata       -1.08559649 -2.793913342  0.848272387 19.6694384
  Magelona papillicornis     -2.59176992 -1.498082094 -0.331266157 16.8718324
  Maldane glebifex           -2.50717000  1.761275610 -0.176802322 16.3263454
  Melinna palmata             0.65235019  2.693794074 -1.235663150  2.7088214
  Microdeutopus gryllotalpa   1.94100174  0.402465759 -2.479615959  0.5458825
  Micromaldane ornithochaeta -0.85996151 -0.847378600 -1.357449211 15.1694240
  Micronephthys stammeri     -1.68067796  0.373874281 -1.377136299 15.5214322
  Microphthalmus fragilis    -1.19933295 -0.311281593  2.807656967 21.5380738
  Microphthalmus sp.         -1.67762648 -4.062668638 -2.984035175  5.7752110
  Monocorophium acherusicum   2.03590220  2.348588824 -3.209772024  1.0582620
  Mytilaster lineatus         3.45792486 -2.876999451 -0.639190554  1.9895849
  Mytilus galloprovincialis  -2.44007336  1.172493110  2.083606770 16.3996400
  Nemertea                    1.88539982 -0.349466806  1.127786695  0.6410157
  Nephtys cirrosa            -1.85773353 -1.029003345  1.938683312 11.7410516
  Nephtys kersivalensis      -2.40554056  0.798954731  2.017808179 15.6776487
  Nereis perivisceralis      -2.43748447 -1.340534174  0.676112949 16.1789847
  Nereis pulsatoria          -0.67325102  2.932654421  1.366148789 20.3085375
  Nototropis guttatus         0.55164072  0.331233431 -1.832712963  6.9021396
  Oligochaeta                 4.78438467 -1.839144882  0.190284877  1.0896891
  Paradoneis harpagonea      -2.67555929  2.076419665 -0.391386610 15.4219440
  Parthenina interstincta    -0.08837407  0.859012747  3.071496088 13.9477704
  Parvicardium exiguum        2.38704769  0.840492912 -0.939434983  1.5860439
  Perinereis cultrifera       0.50722797 -0.113276157 -1.661157517  6.6539819
  Perioculodes longimanus    -0.35461154  1.073104957 -2.669625323  1.4713613
  Phoronida                   0.41760970 -0.104778373  0.768798648  0.9834810
  Phyllodoce sp.             -3.01981147  1.596551836 -2.444205912 13.6076223
  Platyhelminthes             0.13642659  2.048823379  1.017446701  5.2682532
  Platynereis dumerilii       1.16015160  0.817979459 -3.257402370  0.5335618
  Polititapes aureus         -0.31097101 -0.003484991  0.207726167  8.1663775
  Polychaeta larvae          -2.47603970  1.324432120 -2.127596234 17.3670259
  Polydora ciliata            3.32112980  2.466116318 -0.944469824  3.7356192
  Polygordius neapolitanus   -2.56195317  1.459549278 -2.102209971 16.5777513
  Prionospio cirrifera        3.66074027  1.110737308 -0.631746535  3.9722533
  Protodorvillea kefersteini  1.71157203 -2.163161586  0.212721440  2.1815886
  Pseudocuma longicorne      -1.18696326  0.060398177 -0.649119276 12.1140016
  Rissoa membranacea          3.07439563  0.352262377 -1.467873444  1.2519720
  Rissoa splendida           -1.17722111 -1.452549534 -3.971575523  2.2130822
  Salvatoria clavata         -1.10721178 -2.063578713 -4.812044163  0.6526493
  Schistomeringos rudolphi    0.40689157 -1.531835423  4.380316397  5.7291662
  Sphaerosyllis hystrix      -0.25157797 -3.319628032  0.507520309  0.7323123
  Spio filicornis             1.88379434  2.108241421 -2.789507711  3.2010708
  Spisula subtruncata        -1.82096345 -2.397279978 -0.363378203  6.6088708
  Stenosoma capito            1.03034336 -1.189778736 -1.260055108  2.0917511
  Syllis gracilis             1.41729076 -2.384665252  0.383384781  2.7452947
  Syllis hyalina             -1.88202169 -2.749485641 -2.333898090 19.7876482
  Tellina tenuis             -1.53983938 -1.725232702  1.251688339  8.3971338
  Thracia phaseolina         -2.34756969 -1.154151061  0.295338210 15.2506244
  Tricolia pullus            -1.54997095 -3.068171792 -2.263533960  1.1431815
  Tritia neritea             -0.96870731  1.676180384 -1.192815379 14.4417006
  Tritia reticulata           0.14673746  0.035142990  1.051822962  5.4930554
  Turbellaria                 0.39257972  0.926724416 -0.384149662 14.9254496
  Upogebia pusilla           -2.29158763 -2.750765842 -2.772528339 12.5455419

$lv.coefs.mean
                            coefficients
cols                               beta0      theta1      theta2 Dispersion
  Abra alba                   2.13888242  2.02494625  0.00000000  0.9039173
  Abra sp.                   -1.63614385  1.75279647  0.97142025 18.6727291
  Actiniaria                 -2.61691521  1.83563066 -0.38826425 15.6964942
  Alitta succinea             1.27330705  2.97102401 -0.27829396  6.9202135
  Ampelisca diadema           3.99744372  0.17748317 -2.48003918  1.9332675
  Amphibalanus improvisus     1.18019865  3.03403850  0.84069872  1.3428220
  Ampithoe sp.                0.55633234  0.79654712 -1.96331669 11.4652721
  Anadara kagoshimensis      -2.48350809  0.96992778  2.04536933 15.3976554
  Apherusa bispinosa         -2.41244794 -1.22135701  0.37263671 15.7457503
  Apseudopsis ostroumovi      0.49208744 -5.70863561 -2.28849423  2.3600226
  Bittium reticulatum         5.35959523 -2.24730129  2.55918054  0.9033090
  Brachynotus sexdentatus    -1.44045430  0.71450878 -0.16686466 14.9694399
  Capitella capitata          1.05728907 -5.42994083 -0.87630932  1.3938653
  Capitella minima            4.56671016  0.87007774 -2.83628957  0.8594013
  Chamelea gallina           -0.38157154 -3.96601798  0.51825881  0.7698886
  Chironomidae larvae        -2.31951167 -2.51358057 -2.19059104 13.1020303
  Cumella limicola            0.83675508 -4.87676707  0.04294569  0.5384529
  Cumella pygmaea            -1.88064913 -2.56142723  1.43828440 13.8255181
  Cytharella costulata       -0.05882865 -0.48180355 -0.66912987  2.0659951
  Diogenes pugilator         -0.13633737  0.93693479 -2.05136643  0.6737253
  Eteone flava               -2.99229869  1.53699739 -2.31783334 15.4939745
  Eunice vittata             -0.76588621  1.01639552 -1.60645517 16.4582150
  Eurydice dollfusi          -1.47196222 -2.01138668  0.90735311 15.5689613
  Exogone naidina            -0.48294438  0.52010549 -3.32160700 16.2985359
  Gastrosaccus sanctus       -2.40283476 -1.38151330  0.68616297 16.3949157
  Genetyllis tuberculata      0.38774851 -0.11126205  0.34466805 11.6708837
  Glycera sp.                -0.72870491  2.16396196  0.12494862  7.7066628
  Glycera tridactyla         -1.03897216  0.99173487  2.56730843 13.3599830
  Glycera unicornis          -2.43381225  0.72508900  1.86813130 15.7380205
  Harmothoe imbricata        -0.68041216  0.16257029  3.20702790  7.9044696
  Harmothoe reticulata        0.45852799  0.42236334 -0.22853450  1.2825044
  Heteromastus filiformis     3.91591236  0.05721122  0.38292614  0.6521842
  Hirudinea                  -1.07870446  0.09742850  0.79375154 12.4477758
  Hydrobia acuta             -1.44972993  2.70916244 -0.27589184 20.1742310
  Hydrobia sp.               -0.55746024  2.03740809 -0.48343156 17.2761200
  Iphinoe tenella             0.36024416 -0.18870566  0.72218584  8.2563751
  Kellia suborbicularis      -0.40709548 -3.22436862  4.10064828  4.4519858
  Lagis koreni                1.04018203 -0.45308851  3.17096151  0.3874220
  Leiochone leiopygos         0.30437090 -1.84902163  3.28439193  0.6844694
  Lentidium mediterraneum    -2.08118928 -2.18501713  0.13923598 12.7547575
  Lepidochitona cinerea      -2.45175689 -1.39125011  0.37171860 15.5880532
  Loripes orbiculatus         1.92939497 -2.14023283  0.43005116  0.4672440
  Lucinella divaricata       -1.00438545 -2.81804701  0.87379479 18.8822750
  Magelona papillicornis     -2.56498980 -1.56190133 -0.19242780 16.2717609
  Maldane glebifex           -2.52889599  1.83059763 -0.02024547 15.9828841
  Melinna palmata             0.64945353  2.69508273 -1.14664335  3.2922037
  Microdeutopus gryllotalpa   1.99658067  0.35328420 -2.53398369  0.6119471
  Micromaldane ornithochaeta -0.79103597 -0.88253230 -1.37554571 15.5757177
  Micronephthys stammeri     -1.69144296  0.39039090 -1.44368389 15.3044118
  Microphthalmus fragilis    -1.13141238 -0.28718852  2.87945334 20.4531157
  Microphthalmus sp.         -1.66863907 -4.10662368 -2.94165369  8.2221069
  Monocorophium acherusicum   2.12001088  2.31674117 -3.21337569  1.1330927
  Mytilaster lineatus         3.49852852 -2.91783090 -0.67097169  2.0912247
  Mytilus galloprovincialis  -2.50167256  1.06226298  2.06647164 15.8776622
  Nemertea                    1.88145093 -0.33446599  1.16562956  0.7217569
  Nephtys cirrosa            -1.82148290 -1.01085410  1.86246646 12.7306172
  Nephtys kersivalensis      -2.44922572  0.86028687  2.03865338 15.5595031
  Nereis perivisceralis      -2.43317574 -1.40614886  0.73849112 15.8334611
  Nereis pulsatoria          -0.73434139  2.89637927  1.37981303 19.4158083
  Nototropis guttatus         0.55724421  0.26691501 -1.84699017  8.2991262
  Oligochaeta                 4.79216965 -1.84381606  0.18140206  1.1534712
  Paradoneis harpagonea      -2.64922814  2.11201941 -0.29566204 15.1750542
  Parthenina interstincta    -0.09471252  0.79684063  3.08515966 14.4550338
  Parvicardium exiguum        2.39572190  0.87939653 -0.92583614  1.6741525
  Perinereis cultrifera       0.53136124 -0.20341225 -1.69893187  8.0125837
  Perioculodes longimanus    -0.36662280  1.08770077 -2.70897377  2.2195308
  Phoronida                   0.42052141 -0.09234935  0.82955169  1.2652158
  Phyllodoce sp.             -3.06912192  1.54986514 -2.39796130 14.3551043
  Platyhelminthes             0.11430015  2.03070844  1.06486419  6.5782785
  Platynereis dumerilii       1.24539208  0.81537819 -3.29740916  0.6399393
  Polititapes aureus         -0.27442625 -0.07188488  0.32818238 10.0623815
  Polychaeta larvae          -2.54562332  1.23347798 -2.18082502 16.5368246
  Polydora ciliata            3.33321377  2.54083029 -0.97380108  3.9217161
  Polygordius neapolitanus   -2.63386567  1.41497935 -2.08582346 15.9234465
  Prionospio cirrifera        3.63467244  1.12618223 -0.69821552  4.2099250
  Protodorvillea kefersteini  1.72653309 -2.18891654  0.18882661  2.5229508
  Pseudocuma longicorne      -1.10514791  0.06606452 -0.55756864 13.0709803
  Rissoa membranacea          3.11280969  0.32794985 -1.49665055  1.3130619
  Rissoa splendida           -1.19806473 -1.57123744 -4.08526044  3.4369975
  Salvatoria clavata         -1.12281037 -2.17559340 -4.96247687  1.0681004
  Schistomeringos rudolphi    0.40546260 -1.54942598  4.42012037  7.1735283
  Sphaerosyllis hystrix      -0.30251270 -3.44942653  0.64222669  0.9804908
  Spio filicornis             1.93472074  2.05632022 -2.75283745  3.5185236
  Spisula subtruncata        -1.83723210 -2.40962910 -0.39375058  9.0452528
  Stenosoma capito            1.04762649 -1.19526377 -1.27471875  2.3580923
  Syllis gracilis             1.43969512 -2.43665831  0.40281363  3.0307861
  Syllis hyalina             -1.91753021 -2.78946204 -2.40352748 19.0917971
  Tellina tenuis             -1.50907108 -1.76290479  1.30656718 10.3945381
  Thracia phaseolina         -2.32770483 -1.15281135  0.37623343 15.1814811
  Tricolia pullus            -1.60296285 -3.14189463 -2.22543721  2.1314467
  Tritia neritea             -0.90843064  1.65224285 -1.11739715 14.8590041
  Tritia reticulata           0.17054963  0.03729649  1.16150200  6.7376552
  Turbellaria                 0.43410942  0.93798195 -0.44609534 15.6575233
  Upogebia pusilla           -2.28735451 -2.79857754 -2.69501945 13.5721286

$lv.coefs.iqr
                            coefficients
cols                             beta0    theta1    theta2 Dispersion
  Abra alba                  0.8077718 1.0304495 0.0000000  0.6944417
  Abra sp.                   2.2540322 3.5763103 1.1058444 12.2132470
  Actiniaria                 2.0135406 3.1539725 3.5024252 14.6414074
  Alitta succinea            1.2588026 1.7139592 1.7605044  4.6901903
  Ampelisca diadema          0.9445275 1.2002051 0.8861738  0.6844487
  Amphibalanus improvisus    1.1092383 1.2929724 1.3665669  0.9631551
  Ampithoe sp.               1.2965022 2.3757460 1.7934464  8.9749888
  Anadara kagoshimensis      1.9610874 3.1653365 3.2135613 15.1911347
  Apherusa bispinosa         1.9346152 3.5639949 3.5583306 14.1958141
  Apseudopsis ostroumovi     1.0299062 2.1971343 2.3589039  1.4836592
  Bittium reticulatum        0.6060192 1.0460018 1.2398800  0.3620446
  Brachynotus sexdentatus    1.6599766 2.6135836 3.0208975 13.9390023
  Capitella capitata         1.0793509 1.6969070 1.8833356  1.0376971
  Capitella minima           0.9462612 1.1373776 0.9665959  0.3487353
  Chamelea gallina           0.8372801 1.8031965 1.8231069  0.7249800
  Chironomidae larvae        1.8967481 3.0369404 2.8699567 14.7808384
  Cumella limicola           0.8392596 1.5776756 1.7409301  0.5035917
  Cumella pygmaea            1.7067564 2.8466841 3.4567275 14.2059702
  Cytharella costulata       0.7755900 1.3111660 1.3605542  2.1056688
  Diogenes pugilator         0.9829196 1.1719971 1.0649103  0.7396731
  Eteone flava               2.4711481 3.2582702 2.7222001 15.2432277
  Eunice vittata             1.6914053 2.3099629 2.8262074 13.9317893
  Eurydice dollfusi          1.6836070 3.2775192 3.3949566 13.6076075
  Exogone naidina            1.6740535 3.1661563 2.4348108 11.9380552
  Gastrosaccus sanctus       2.0261497 3.5082370 3.4269858 13.9227408
  Genetyllis tuberculata     1.1731400 2.3994804 1.8661358  9.3463257
  Glycera sp.                1.2737038 2.0484646 2.1532391  8.6122500
  Glycera tridactyla         1.7029519 2.8407708 3.0902686 12.8021393
  Glycera unicornis          2.0413318 3.4036766 3.3136065 14.1695923
  Harmothoe imbricata        1.2915250 2.6097106 2.6100673  8.6488703
  Harmothoe reticulata       0.7458101 1.1338388 1.1189780  1.3308373
  Heteromastus filiformis    0.6178348 0.6152292 0.6293157  0.2623211
  Hirudinea                  1.4742449 2.7463893 2.6418280 14.3634015
  Hydrobia acuta             2.0430084 2.9196522 3.4689480 10.0291567
  Hydrobia sp.               1.7310303 2.4912074 3.2731602 13.1158066
  Iphinoe tenella            0.9847199 2.2131061 2.0977872  6.4155572
  Kellia suborbicularis      1.2806073 2.3748090 2.6267318  4.2371698
  Lagis koreni               0.7888489 1.3773115 1.2851926  0.4025635
  Leiochone leiopygos        0.8610489 1.7070016 1.8213552  0.6762818
  Lentidium mediterraneum    1.7602359 2.9142245 3.2676259 15.2191966
  Lepidochitona cinerea      2.0556550 3.1633930 3.5220440 14.0013844
  Loripes orbiculatus        0.5703296 0.9120636 0.9686539  0.3656034
  Lucinella divaricata       1.7568803 3.2228774 3.5865186 10.8744911
  Magelona papillicornis     1.9556453 3.2635256 3.4418043 13.6699525
  Maldane glebifex           1.9193178 3.2456566 3.3420779 14.0348865
  Melinna palmata            0.9935666 1.6796262 1.4115756  2.6648394
  Microdeutopus gryllotalpa  0.8569135 1.0395300 0.7651328  0.4269162
  Micromaldane ornithochaeta 1.6280628 2.8196837 2.5771964 12.8939136
  Micronephthys stammeri     1.6809213 2.8472356 3.1241337 14.7376100
  Microphthalmus fragilis    1.9963919 3.8691929 3.2596675 10.2471433
  Microphthalmus sp.         1.8504550 2.9197304 2.7555891  9.6973564
  Monocorophium acherusicum  1.1358168 1.2785906 1.0608438  0.6077650
  Mytilaster lineatus        0.6643706 1.1497128 1.3575011  0.8498367
  Mytilus galloprovincialis  2.0240982 3.4580309 3.2668847 15.0458032
  Nemertea                   0.6248592 0.8761647 0.8771191  0.5067207
  Nephtys cirrosa            1.6656881 3.1051659 3.0414807 14.3076043
  Nephtys kersivalensis      2.0147372 3.5732922 3.4109915 15.3859008
  Nereis perivisceralis      2.0584389 3.1260971 3.5560068 14.7663716
  Nereis pulsatoria          2.0567647 3.1961618 2.9473474 11.8172201
  Nototropis guttatus        1.1646901 1.7365468 2.0837510  6.0615746
  Oligochaeta                0.5259047 0.8305961 0.8441557  0.4244848
  Paradoneis harpagonea      2.1444022 2.9612037 3.2278836 15.1383733
  Parthenina interstincta    1.5055468 2.6346828 3.0807665 11.8873072
  Parvicardium exiguum       0.7850171 1.0750322 0.7483103  0.7293900
  Perinereis cultrifera      1.0805323 1.6329966 2.1062774  6.1840593
  Perioculodes longimanus    1.1032982 1.4716278 1.2378072  2.2119809
  Phoronida                  0.7594325 1.1630404 1.2804140  1.3019866
  Phyllodoce sp.             2.2550550 3.0735605 2.9394432 15.9314172
  Platyhelminthes            1.1563907 1.6487311 2.0807245  6.0944242
  Platynereis dumerilii      0.9992105 1.2208925 0.9684694  0.5628459
  Polititapes aureus         1.1458294 2.3230930 2.4226906 10.1367425
  Polychaeta larvae          2.1619038 3.4823055 2.9956421 13.8947030
  Polydora ciliata           1.0043883 1.3138186 1.4181004  1.8698192
  Polygordius neapolitanus   2.1546835 3.2961698 3.0338104 14.4563501
  Prionospio cirrifera       0.9502773 1.3963345 1.6280236  1.7239597
  Protodorvillea kefersteini 0.6818089 1.2469220 1.7766697  1.6098308
  Pseudocuma longicorne      1.5064578 2.3642233 2.7644187 13.4495182
  Rissoa membranacea         0.8013119 0.9709186 0.7399376  0.4723165
  Rissoa splendida           1.2503066 2.1301488 1.6836482  3.3194925
  Salvatoria clavata         1.2646202 2.1061699 1.7758818  1.1461714
  Schistomeringos rudolphi   1.2380350 2.4683331 2.8235987  5.8850475
  Sphaerosyllis hystrix      0.8458007 1.8065492 1.8052376  1.0028242
  Spio filicornis            1.1682502 1.8453695 1.4447831  1.7017632
  Spisula subtruncata        1.5765267 2.7105547 2.9447013 11.0581671
  Stenosoma capito           0.7967887 1.4746078 1.4427902  1.2922306
  Syllis gracilis            0.8029568 1.6814493 1.4794253  1.5894228
  Syllis hyalina             2.2488821 3.2611275 3.3268882 11.5860079
  Tellina tenuis             1.4304167 3.0670900 3.0674947 12.1919540
  Thracia phaseolina         1.8712442 3.1851556 3.3067078 15.2466140
  Tricolia pullus            1.3467969 2.2993183 1.9832650  2.1179135
  Tritia neritea             1.6338762 2.5048116 2.9800935 12.8432740
  Tritia reticulata          1.0453193 1.9839105 2.2849369  5.4672029
  Turbellaria                1.3468811 2.0611374 2.5864368 11.3982121
  Upogebia pusilla           2.0364368 3.1703656 3.2171938 13.8653851

$lv.coefs.sd
                            coefficients
cols                             beta0    theta1    theta2 Dispersion
  Abra alba                  0.6179206 0.7341573 0.0000000  0.5547260
  Abra sp.                   1.7269819 2.7193223 0.8959785  7.7696513
  Actiniaria                 1.5748771 2.3530683 2.5557356  8.6548663
  Alitta succinea            0.9770620 1.3625463 1.4226317  4.0693374
  Ampelisca diadema          0.6048811 0.9247662 0.7037473  0.5106893
  Amphibalanus improvisus    0.7691414 0.9560101 0.9997657  0.9212057
  Ampithoe sp.               1.0822354 1.7884225 1.4307216  6.4905188
  Anadara kagoshimensis      1.6159764 2.5030083 2.3982778  8.7951927
  Apherusa bispinosa         1.4821613 2.5764010 2.5847672  8.5382822
  Apseudopsis ostroumovi     0.8648580 1.7479676 1.6878551  1.3793725
  Bittium reticulatum        0.4481639 0.8471717 0.9020066  0.2960943
  Brachynotus sexdentatus    1.3100271 2.0084626 2.5095365  8.3060120
  Capitella capitata         0.8018958 1.2985538 1.5027197  0.9647219
  Capitella minima           0.6680849 0.8531485 0.6835401  0.2784175
  Chamelea gallina           0.6940095 1.3874466 1.3469307  0.8420455
  Chironomidae larvae        1.4780975 2.2933741 2.2941830  8.6470509
  Cumella limicola           0.6335681 1.2139391 1.3361393  0.4429862
  Cumella pygmaea            1.3537705 2.2778549 2.5775134  8.3677398
  Cytharella costulata       0.5753893 1.0141772 1.0403629  2.2027991
  Diogenes pugilator         0.6849581 0.9038170 0.8491618  0.7653291
  Eteone flava               1.8528141 2.4883189 2.1624537  8.7578086
  Eunice vittata             1.3143207 1.8637859 2.2095959  7.9688584
  Eurydice dollfusi          1.2926469 2.4378341 2.6336105  8.1921475
  Exogone naidina            1.2743444 2.4131870 1.8652715  7.2616760
  Gastrosaccus sanctus       1.5612049 2.4978258 2.6553574  8.4078812
  Genetyllis tuberculata     0.9435342 1.8690500 1.4779616  6.8902846
  Glycera sp.                0.9709714 1.7162658 1.6620435  6.7831387
  Glycera tridactyla         1.2972348 2.2866306 2.3967152  7.9713687
  Glycera unicornis          1.5415704 2.5776893 2.5399018  8.3953916
  Harmothoe imbricata        1.0588286 1.9606180 2.0622513  6.6690862
  Harmothoe reticulata       0.5626646 0.9077461 0.9071224  1.1737408
  Heteromastus filiformis    0.4540283 0.4914411 0.4739231  0.2101454
  Hirudinea                  1.1682084 2.1968187 2.1102681  8.4954456
  Hydrobia acuta             1.6622399 2.4363711 2.6516021  6.6926237
  Hydrobia sp.               1.3324880 1.8774994 2.4577814  7.8868605
  Iphinoe tenella            0.8456904 1.7385084 1.6898866  5.4297621
  Kellia suborbicularis      1.0277261 1.9203204 2.0481014  4.0017403
  Lagis koreni               0.6509170 1.0550806 0.9409469  0.3587964
  Leiochone leiopygos        0.6519512 1.2959249 1.3109019  0.6509516
  Lentidium mediterraneum    1.3539198 2.1966293 2.4514373  8.7306384
  Lepidochitona cinerea      1.5324638 2.4966328 2.6521245  8.5456789
  Loripes orbiculatus        0.3959749 0.6927468 0.7799285  0.3124113
  Lucinella divaricata       1.3763227 2.4777882 2.6776544  6.8400431
  Magelona papillicornis     1.5565367 2.3381116 2.5928660  8.2944323
  Maldane glebifex           1.5448785 2.4766086 2.5917259  8.3729674
  Melinna palmata            0.7952699 1.3679320 1.1355752  2.4075626
  Microdeutopus gryllotalpa  0.5839310 0.7465754 0.5832198  0.3727887
  Micromaldane ornithochaeta 1.2617490 2.1376684 2.0555395  7.9878402
  Micronephthys stammeri     1.3637490 2.1331429 2.4083291  8.5042296
  Microphthalmus fragilis    1.5033577 2.7800848 2.4539419  6.7412717
  Microphthalmus sp.         1.4920093 2.1236451 2.1042801  7.4568993
  Monocorophium acherusicum  0.7560800 0.9833146 0.8344086  0.5115369
  Mytilaster lineatus        0.4893444 1.0118652 1.0113182  0.6871337
  Mytilus galloprovincialis  1.5895827 2.6292268 2.4474274  8.6117594
  Nemertea                   0.4720183 0.6896806 0.7003839  0.4234338
  Nephtys cirrosa            1.3221287 2.2855199 2.3323289  8.6253573
  Nephtys kersivalensis      1.5829312 2.6397244 2.5712667  8.8739685
  Nereis perivisceralis      1.5660467 2.3688512 2.6245307  8.4236208
  Nereis pulsatoria          1.4702990 2.3307387 2.3236206  7.1611983
  Nototropis guttatus        0.8882552 1.3792482 1.7563265  5.3414875
  Oligochaeta                0.3859186 0.5865456 0.6790956  0.3555510
  Paradoneis harpagonea      1.6566954 2.3354595 2.5602696  8.6282503
  Parthenina interstincta    1.1543617 2.0487979 2.3090967  7.3885945
  Parvicardium exiguum       0.5514123 0.7976999 0.6096550  0.5844940
  Perinereis cultrifera      0.8449069 1.3087897 1.6771366  5.2671665
  Perioculodes longimanus    0.7900576 1.1596241 0.9765467  2.4041500
  Phoronida                  0.5718865 0.8893804 1.0249754  1.1170671
  Phyllodoce sp.             1.8012534 2.3878749 2.1799716  8.9290385
  Platyhelminthes            0.9304663 1.3697593 1.6409519  5.1219709
  Platynereis dumerilii      0.6810220 0.9015320 0.7208040  0.4833017
  Polititapes aureus         0.9144046 1.8825972 1.8877419  7.1997284
  Polychaeta larvae          1.7593668 2.6309557 2.2660580  8.3103666
  Polydora ciliata           0.7579670 1.0692822 1.1084382  1.4447361
  Polygordius neapolitanus   1.7398891 2.5286733 2.3122050  8.4491657
  Prionospio cirrifera       0.6802857 1.0458808 1.1931745  1.4564417
  Protodorvillea kefersteini 0.5426101 0.9864639 1.4039943  1.4059962
  Pseudocuma longicorne      1.2020334 1.8973242 2.2191991  8.3169721
  Rissoa membranacea         0.5302404 0.7471367 0.5753379  0.3931313
  Rissoa splendida           1.0318005 1.7065140 1.3939843  3.8760434
  Salvatoria clavata         0.9811041 1.5626914 1.3611385  1.1832013
  Schistomeringos rudolphi   1.0343874 1.9479129 2.1887793  5.1305187
  Sphaerosyllis hystrix      0.6732918 1.3752817 1.3045463  0.9054008
  Spio filicornis            0.8288796 1.3528050 1.0763145  1.5326535
  Spisula subtruncata        1.2428276 2.1647286 2.2864516  7.8116135
  Stenosoma capito           0.5739867 1.1329663 1.1181004  1.2450259
  Syllis gracilis            0.5518862 1.2288917 1.1197247  1.4578930
  Syllis hyalina             1.7656095 2.4193458 2.4116352  7.1813048
  Tellina tenuis             1.1480275 2.2332793 2.3638641  8.1593453
  Thracia phaseolina         1.4568604 2.5279476 2.5255955  8.7178708
  Tricolia pullus            0.9675243 1.7187464 1.6238935  2.9683862
  Tritia neritea             1.2748872 1.9417881 2.2863807  7.8401214
  Tritia reticulata          0.8096867 1.5740717 1.7548478  5.0588477
  Turbellaria                1.0467009 1.6020642 1.9419780  7.0924721
  Upogebia pusilla           1.5692006 2.2812504 2.3562549  8.3759696

$row.coefs
$row.coefs[[1]]
$row.coefs[[1]]$median
         1          2          3          4          5 
-1.5607773 -0.9632179 -2.7394831 -0.9652821 -0.9995208 

$row.coefs[[1]]$mean
         1          2          3          4          5 
-1.5330344 -0.9464873 -2.7323938 -0.9324430 -0.9980401 

$row.coefs[[1]]$iqr
        1         2         3         4         5 
0.5409534 0.5820383 0.7628854 0.6816993 0.7356074 

$row.coefs[[1]]$sd
        1         2         3         4         5 
0.3928366 0.3990326 0.5300180 0.4531568 0.5234757 



$hpdintervals
$hpdintervals$lv
, , type = lower

    lv
rows         lv1         lv2
  1   0.23292869 -0.82194469
  2   0.21891986 -0.71798890
  3   0.10447471 -0.98864250
  4   0.14009828 -0.65729739
  5  -0.04247357 -0.01552904
  6  -0.10664364  0.04052210
  7  -0.01108422  0.07577619
  8   0.02877648 -0.17809693
  9   0.01862386 -0.45758020
  10 -0.06537411 -0.37882292
  11 -0.40127107 -0.63335985
  12  0.01616270 -0.38404551
  13 -0.35058439  0.09667652
  14 -0.12407609 -0.02198392
  15 -0.25448407  0.03675943
  16 -0.41607692 -0.05595725
  17 -0.31660719 -1.40614023
  18 -0.18413879 -1.39918931
  19 -0.14830582 -1.72074955
  20 -0.32644118 -1.66123691
  21 -0.82412123 -0.54476415
  22 -0.71035996 -0.31704279
  23 -0.69332959 -0.41885082
  24 -0.54775804 -0.28201333
  25 -0.62333610 -0.36678655
  26 -0.70621675 -0.22151172
  27 -0.78458377 -0.26904734
  28 -0.89084920 -0.25036404
  29 -0.87465686 -0.96928203
  30 -0.95038506 -1.00274346
  31 -0.67700431 -0.66734502
  32 -0.78463920 -0.78686401

, , type = upper

    lv
rows         lv1         lv2
  1   1.14170376  0.24079800
  2   1.09207236  0.37173019
  3   0.98516004  0.05199271
  4   0.98329871  0.32829649
  5   0.70224945  0.86313380
  6   0.66175577  0.86209203
  7   0.77801155  0.89910529
  8   0.76063623  0.69005641
  9   0.66717454  0.34439572
  10  0.65068173  0.44310903
  11  0.30646194  0.09398513
  12  0.74149068  0.48895019
  13  0.38719627  0.84058630
  14  0.56498067  0.71770681
  15  0.44234359  0.76644883
  16  0.15903374  0.60397609
  17  1.02681602 -0.38081570
  18  1.15178564 -0.32178470
  19  1.35585708 -0.55660524
  20  1.10405383 -0.59383270
  21 -0.20396495  0.17383039
  22 -0.08687165  0.38229868
  23 -0.11599517  0.30605377
  24  0.01597480  0.40803590
  25 -0.06386525  0.28338450
  26 -0.15104229  0.47812561
  27 -0.26485346  0.50890152
  28 -0.21711919  0.51205506
  29 -0.15077257 -0.24452804
  30 -0.19180441 -0.27605208
  31 -0.03290289  0.02279252
  32 -0.10209206 -0.05334919


$hpdintervals$lv.coefs
, , type = lower

                            coefficients
cols                               beta0      theta1        theta2   Dispersion
  Abra alba                   0.93135368  0.69395297  0.0000000000 6.599801e-02
  Abra sp.                   -4.93328339 -3.55698089  0.0009026882 4.000080e+00
  Actiniaria                 -6.20667744 -2.68603715 -5.2148290137 7.890785e-01
  Alitta succinea            -0.64983087  0.23712271 -2.9857875381 9.207851e-01
  Ampelisca diadema           3.01593209 -1.83657998 -4.0557211213 1.071973e+00
  Amphibalanus improvisus    -0.17895430  1.23380103 -1.2104510578 9.435485e-02
  Ampithoe sp.               -1.33524645 -3.08065247 -4.6585176250 2.058939e+00
  Anadara kagoshimensis      -5.81478098 -3.81666711 -2.7215550157 1.601287e+00
  Apherusa bispinosa         -5.33407609 -6.03444118 -4.5760288633 1.324696e+00
  Apseudopsis ostroumovi     -1.17766864 -9.31320124 -5.3151275527 4.373719e-01
  Bittium reticulatum         4.55055217 -4.08162967  0.8198470038 4.645416e-01
  Brachynotus sexdentatus    -3.81802712 -2.82849021 -5.7091686479 2.396990e+00
  Capitella capitata         -0.41573772 -7.86096887 -3.9869592075 4.474075e-03
  Capitella minima            3.54614402 -0.84824017 -4.2305100762 3.930415e-01
  Chamelea gallina           -1.62120350 -6.55743066 -1.9877939040 2.724228e-03
  Chironomidae larvae        -5.26598790 -6.97167667 -6.7818014050 1.097818e-01
  Cumella limicola           -0.37761799 -7.23930738 -2.1778401195 1.687386e-03
  Cumella pygmaea            -4.54872797 -7.02023545 -3.5903688721 6.397994e-01
  Cytharella costulata       -1.16335071 -2.63419341 -2.5960943867 2.748654e-03
  Diogenes pugilator         -1.39199154 -0.86517946 -3.7731525745 1.467822e-03
  Eteone flava               -6.53022348 -3.31045722 -7.0080166767 5.399786e-01
  Eunice vittata             -3.19174990 -2.44148654 -6.0055352376 3.723655e+00
  Eurydice dollfusi          -3.99066566 -6.33810180 -4.1547387665 2.489398e+00
  Exogone naidina            -3.17960668 -4.27550553 -6.7070009281 5.203934e+00
  Gastrosaccus sanctus       -5.66522583 -5.80785539 -4.1360604763 2.300937e+00
  Genetyllis tuberculata     -1.38390843 -3.86820621 -2.4779221126 2.010344e+00
  Glycera sp.                -2.67164026 -1.17565807 -2.9689647544 1.155972e-02
  Glycera tridactyla         -3.55909363 -3.52049543 -2.0704139725 9.541797e-01
  Glycera unicornis          -5.44034560 -4.57988830 -2.7517642751 2.292254e+00
  Harmothoe imbricata        -2.74313595 -3.71187088 -1.2788466315 2.226736e-03
  Harmothoe reticulata       -0.57543594 -1.41146714 -1.9322382345 9.370507e-05
  Heteromastus filiformis     3.02473815 -0.86093526 -0.4535290622 3.101535e-01
  Hirudinea                  -3.47128776 -4.09249707 -3.1638468615 1.604591e-01
  Hydrobia acuta             -4.50428251 -2.26127084 -5.4064056563 7.349489e+00
  Hydrobia sp.               -3.48957612 -1.70266281 -5.4552365710 3.685232e+00
  Iphinoe tenella            -1.40324872 -3.88150818 -2.5236814195 8.443675e-01
  Kellia suborbicularis      -2.36347500 -7.41568104 -0.3899770175 8.285002e-03
  Lagis koreni               -0.27691973 -2.37286768  1.5037555458 1.492204e-03
  Leiochone leiopygos        -0.97709619 -4.38993798  0.9603582813 6.355268e-03
  Lentidium mediterraneum    -4.95336423 -6.73896049 -4.7414336741 3.702229e-02
  Lepidochitona cinerea      -5.34812599 -6.06364941 -5.1756484560 1.713815e+00
  Loripes orbiculatus         1.17359716 -3.52468889 -0.9876350450 1.735010e-02
  Lucinella divaricata       -3.52042139 -8.01534497 -3.7741248288 6.644234e+00
  Magelona papillicornis     -5.56007224 -6.59257239 -5.0062522595 2.181389e+00
  Maldane glebifex           -5.42267781 -2.99432974 -5.0260887262 2.390346e+00
  Melinna palmata            -0.93611297 -0.01189583 -3.4355901694 3.626634e-02
  Microdeutopus gryllotalpa   0.94980861 -1.06256483 -3.7044950325 5.718521e-02
  Micromaldane ornithochaeta -3.06232329 -5.26593201 -5.3207278023 3.129105e+00
  Micronephthys stammeri     -4.25846565 -3.90922459 -6.1112285046 9.357713e-01
  Microphthalmus fragilis    -4.18237282 -5.74148652 -1.7365237412 7.567979e+00
  Microphthalmus sp.         -4.77337819 -8.41766311 -6.7489981433 2.269304e-02
  Monocorophium acherusicum   0.79164097  0.41891633 -4.7869913555 2.725585e-01
  Mytilaster lineatus         2.64585603 -4.86652627 -2.8324285697 8.645731e-01
  Mytilus galloprovincialis  -5.89587952 -4.43737780 -2.7741234691 2.122127e+00
  Nemertea                    0.98427149 -1.77587582 -0.1213472828 4.249048e-02
  Nephtys cirrosa            -4.46026497 -5.81716903 -2.5743053446 6.301529e-03
  Nephtys kersivalensis      -5.56974297 -4.01340674 -3.1653836057 1.429294e+00
  Nereis perivisceralis      -5.28656783 -5.82144722 -4.2097329966 2.628135e+00
  Nereis pulsatoria          -3.51691654 -1.53917589 -3.1081968606 6.369624e+00
  Nototropis guttatus        -1.21468026 -2.60132235 -5.5424157848 9.909077e-01
  Oligochaeta                 4.09146020 -2.98521507 -1.1682713457 5.438464e-01
  Paradoneis harpagonea      -6.30025423 -2.40710878 -5.2935106086 1.270593e+00
  Parthenina interstincta    -2.26973330 -3.28671353 -1.7135494496 3.132267e+00
  Parvicardium exiguum        1.33579509 -0.54703968 -2.2354798639 7.169506e-01
  Perinereis cultrifera      -1.14484191 -2.69379963 -4.8175445404 1.175520e+00
  Perioculodes longimanus    -1.90175878 -1.00035503 -4.6909167903 1.192765e-03
  Phoronida                  -0.57774859 -1.83384582 -0.9369852644 8.534155e-04
  Phyllodoce sp.             -6.89758113 -3.02637122 -6.6628621167 3.853221e-01
  Platyhelminthes            -1.78314786 -0.47405802 -2.1053016889 1.854631e-01
  Platynereis dumerilii       0.15996454 -0.77476101 -4.7414339546 1.216555e-03
  Polititapes aureus         -1.94630613 -3.78046118 -3.4284460943 4.448733e-02
  Polychaeta larvae          -5.79047761 -3.73503861 -6.5651036613 2.629540e+00
  Polydora ciliata            1.85344674  0.34396155 -3.2052372570 1.616695e+00
  Polygordius neapolitanus   -6.28148180 -4.15718083 -6.2825248991 1.932298e+00
  Prionospio cirrifera        2.23700950 -0.87894537 -3.0306760352 1.766141e+00
  Protodorvillea kefersteini  0.71470576 -4.18638203 -2.5756653424 6.511765e-01
  Pseudocuma longicorne      -3.37512167 -3.43369094 -4.8569330236 1.436336e-01
  Rissoa membranacea          2.11188846 -1.12536041 -2.5469398243 5.629835e-01
  Rissoa splendida           -3.12359075 -5.25585533 -7.2244334667 4.791006e-03
  Salvatoria clavata         -2.89255481 -5.23218424 -7.8856038489 4.570989e-04
  Schistomeringos rudolphi   -1.68291573 -5.41310681  0.2220915282 5.269437e-01
  Sphaerosyllis hystrix      -1.57747874 -6.24518614 -1.8268728602 4.301480e-03
  Spio filicornis             0.48529291 -0.65702539 -4.7659825548 1.040910e+00
  Spisula subtruncata        -4.32313300 -6.73195588 -4.6756394305 8.575949e-03
  Stenosoma capito            0.00841506 -3.23601154 -3.4331783095 5.302337e-01
  Syllis gracilis             0.37569458 -4.93020449 -1.7127074920 1.081708e+00
  Syllis hyalina             -5.59332614 -7.72932913 -7.0555497635 6.506526e+00
  Tellina tenuis             -3.71583644 -5.92231262 -3.1460995668 2.604122e-02
  Thracia phaseolina         -5.26293758 -6.50217775 -4.1906798576 9.642613e-01
  Tricolia pullus            -3.45124822 -6.63392411 -5.5174098811 7.854921e-03
  Tritia neritea             -3.31699167 -2.30836241 -5.6202143748 2.404856e+00
  Tritia reticulata          -1.50969171 -3.08164335 -2.2941613148 4.128096e-01
  Turbellaria                -1.46414201 -2.27919726 -4.5472122754 4.224548e+00
  Upogebia pusilla           -5.58160423 -7.33796546 -6.8360274704 2.430044e-01

, , type = upper

                            coefficients
cols                             beta0     theta1     theta2 Dispersion
  Abra alba                  3.3197606  3.5645378  0.0000000   1.976909
  Abra sp.                   1.7226800  7.0121781  2.7566974  29.974889
  Actiniaria                 0.1792224  6.2177340  4.4228309  29.108536
  Alitta succinea            3.1950994  5.6157629  2.4273088  14.745797
  Ampelisca diadema          5.1614323  1.8238073 -1.1579983   2.960174
  Amphibalanus improvisus    2.6046571  4.9659784  2.6987352   3.040911
  Ampithoe sp.               2.6760656  3.8579294  1.0378502  24.975696
  Anadara kagoshimensis      0.8665543  5.8171492  6.6931995  29.917469
  Apherusa bispinosa         0.4869555  3.5080455  5.4817859  29.469136
  Apseudopsis ostroumovi     2.3636254 -2.3563788  1.2223852   5.143912
  Bittium reticulatum        6.2101514 -0.5995671  4.2590097   1.558321
  Brachynotus sexdentatus    1.3330468  5.0596953  4.3566334  29.979605
  Capitella capitata         2.6917506 -2.7563614  1.9095968   3.342419
  Capitella minima           6.0176398  2.4776267 -1.6146435   1.423626
  Chamelea gallina           1.1269001 -1.2116889  3.3191836   2.340091
  Chironomidae larvae        0.5512231  2.0191462  2.2081978  27.745524
  Cumella limicola           2.0189770 -2.5934611  3.0627129   1.305172
  Cumella pygmaea            0.8190638  1.7604833  6.3195921  28.095591
  Cytharella costulata       1.0173281  1.3674215  1.4076895   6.158779
  Diogenes pugilator         1.1425094  2.6803757 -0.4070868   2.112171
  Eteone flava               0.5772902  6.2737233  1.5931189  28.810042
  Eunice vittata             1.9071270  4.7715223  2.5670558  29.849691
  Eurydice dollfusi          1.2409188  2.9293265  5.9891445  29.836992
  Exogone naidina            2.0038740  5.1156578  0.4409653  29.974801
  Gastrosaccus sanctus       0.3903367  3.9410478  6.5224242  29.988260
  Genetyllis tuberculata     2.1865903  3.4423451  3.6171705  27.090741
  Glycera sp.                1.0687582  5.7493051  3.5284808  22.293641
  Glycera tridactyla         1.5058664  5.7575407  7.3283992  28.241998
  Glycera unicornis          0.6804678  5.6322599  7.3838996  29.910210
  Harmothoe imbricata        1.5315707  3.7145459  6.8416256  21.893109
  Harmothoe reticulata       1.5439608  2.0769663  1.6086929   3.730054
  Heteromastus filiformis    4.7799436  1.0312328  1.4198749   1.108586
  Hirudinea                  1.1181332  4.7726220  5.1988738  27.753842
  Hydrobia acuta             2.1783766  7.5179800  5.0572814  29.989080
  Hydrobia sp.               1.8872469  5.6093893  4.1078983  29.933309
  Iphinoe tenella            1.9829394  2.9368719  4.2920647  19.607836
  Kellia suborbicularis      1.6731654  0.1357781  7.8896399  12.345176
  Lagis koreni               2.3467228  1.8632398  5.0204543   1.096612
  Leiochone leiopygos        1.5223817  0.5955029  5.8669703   2.009575
  Lentidium mediterraneum    0.5023478  1.9292461  5.0871782  27.810662
  Lepidochitona cinerea      0.7220257  4.0051651  5.2399700  29.857372
  Loripes orbiculatus        2.6557056 -0.8699264  2.1235508   1.050349
  Lucinella divaricata       1.8339136  1.8479387  6.9822060  29.787075
  Magelona papillicornis     0.5119025  2.4399388  4.9501528  29.875577
  Maldane glebifex           0.5274868  6.4510835  5.2135011  29.923588
  Melinna palmata            2.0889788  5.3644373  0.9812852   7.649165
  Microdeutopus gryllotalpa  3.0963473  1.7616995 -1.4326157   1.251763
  Micromaldane ornithochaeta 1.7969152  3.1472728  2.8103118  29.940172
  Micronephthys stammeri     1.1385447  4.2862899  3.1706291  28.879952
  Microphthalmus fragilis    1.6361270  4.7939551  7.9489913  29.940053
  Microphthalmus sp.         1.2474833 -0.2524266  1.3297215  24.480486
  Monocorophium acherusicum  3.6258465  4.2641140 -1.4518093   2.160868
  Mytilaster lineatus        4.5238079 -0.9076060  1.1005903   3.359699
  Mytilus galloprovincialis  0.4890444  6.0601991  6.7014891  29.999734
  Nemertea                   2.8019617  0.9836751  2.6435071   1.542586
  Nephtys cirrosa            0.7207251  3.1311315  6.3747781  27.640527
  Nephtys kersivalensis      0.4067579  6.3455155  6.6776896  29.983413
  Nereis perivisceralis      0.7060812  3.3699627  6.0908050  29.957390
  Nereis pulsatoria          2.1004808  7.2288398  5.7588087  29.964603
  Nototropis guttatus        2.2231547  2.8660047  1.5790043  19.613819
  Oligochaeta                5.5941070 -0.7806772  1.5335991   1.829618
  Paradoneis harpagonea      0.3441335  7.0005457  4.7262809  29.583742
  Parthenina interstincta    2.1081351  4.7247564  7.1465968  29.198145
  Parvicardium exiguum       3.3705743  2.6290818  0.2075728   2.885092
  Perinereis cultrifera      2.1446200  2.2633266  1.6099145  19.393359
  Perioculodes longimanus    1.0753820  3.6315489 -0.7982055   6.826097
  Phoronida                  1.5774166  1.6452499  3.1356161   3.384461
  Phyllodoce sp.             0.1670279  6.3206142  1.7485095  28.761561
  Platyhelminthes            1.9333640  5.2160605  4.1770984  17.051040
  Platynereis dumerilii      2.6507128  2.6096868 -1.9402828   1.621257
  Polititapes aureus         1.6621329  3.8858462  3.9442116  24.611347
  Polychaeta larvae          1.4021273  6.0600633  2.1753616  29.967005
  Polydora ciliata           4.7837898  4.6267739  1.0758848   6.892951
  Polygordius neapolitanus   0.6088371  5.8923380  2.7329258  29.760870
  Prionospio cirrifera       4.8226443  3.1209575  1.5388422   6.878124
  Protodorvillea kefersteini 2.7960796 -0.3879756  2.8703220   5.408724
  Pseudocuma longicorne      1.4374976  4.0882483  3.8746699  27.827786
  Rissoa membranacea         4.0460372  1.8296713 -0.3268782   2.058737
  Rissoa splendida           0.9707741  1.4093826 -1.6580596  11.031501
  Salvatoria clavata         0.8723437  0.7227943 -2.7096110   3.588916
  Schistomeringos rudolphi   2.3247152  2.4087365  8.9136816  17.949596
  Sphaerosyllis hystrix      1.0577982 -0.9147981  3.2397818   2.806042
  Spio filicornis            3.6556148  4.5136035 -0.5095093   6.661942
  Spisula subtruncata        0.6758760  1.9174845  4.1907814  25.475998
  Stenosoma capito           2.1400922  1.1675043  0.9170840   4.939115
  Syllis gracilis            2.5231102 -0.2276065  2.7496755   5.937299
  Syllis hyalina             1.4293439  1.5945567  2.1744217  29.988708
  Tellina tenuis             0.5456396  2.6080885  5.9297081  26.969072
  Thracia phaseolina         0.3842891  3.3702319  5.5699964  29.275729
  Tricolia pullus            0.2044710 -0.2044962  1.1057326   7.742245
  Tritia neritea             1.6673078  5.2949033  3.3046977  29.404724
  Tritia reticulata          1.7229859  3.1557802  4.7834694  17.476177
  Turbellaria                2.6051122  4.1715489  2.9780193  28.857069
  Upogebia pusilla           0.5616703  1.3111608  2.2970976  28.219621


$hpdintervals$row.coefs
$hpdintervals$row.coefs[[1]]
      lower       upper
1 -2.241429 -0.75037346
2 -1.731546 -0.22037479
3 -3.660101 -1.67121377
4 -1.793684 -0.06723921
5 -1.986481  0.03685933



$call
boral.default(y = zoo.abnd.flt.zostera, family = "negative.binomial", 
    lv.control = list(num.lv = 2), row.eff = "fixed", row.ids = matrix(rep(1:5, 
        times = c(8, 8, 4, 8, 4)), ncol = 1))

$n
[1] 32

$p
[1] 94

$X.ind
numeric(0)

$y

$row.eff
[1] "fixed"

$row.ids
      [,1]
 [1,]    1
 [2,]    1
 [3,]    1
 [4,]    1
 [5,]    1
 [6,]    1
 [7,]    1
 [8,]    1
 [9,]    2
[10,]    2
[11,]    2
[12,]    2
[13,]    2
[14,]    2
[15,]    2
[16,]    2
[17,]    3
[18,]    3
[19,]    3
[20,]    3
[21,]    4
[22,]    4
[23,]    4
[24,]    4
[25,]    4
[26,]    4
[27,]    4
[28,]    4
[29,]    5
[30,]    5
[31,]    5
[32,]    5

$geweke.diag
$geweke.diag$geweke.diag
$geweke.diag$geweke.diag$lv.coefs
                                  beta0   Disperson
Abra alba                   2.110296367  0.30583945
Abra sp.                   -0.557686362  0.08600817
Actiniaria                 -0.317139957  0.51098099
Alitta succinea             1.777557277 -0.71919911
Ampelisca diadema           0.365079671  1.74591150
Amphibalanus improvisus     1.763951641  0.55654682
Ampithoe sp.               -0.335884553 -0.78823183
Anadara kagoshimensis       1.602232678 -0.90871219
Apherusa bispinosa          1.628280309  1.40871665
Apseudopsis ostroumovi      0.416488899  1.07447579
Bittium reticulatum         0.845854806  0.62486284
Brachynotus sexdentatus     1.897747693  0.96495437
Capitella capitata          0.588103331 -0.24991175
Capitella minima            0.846923335  0.13500279
Chamelea gallina           -0.705841477  0.13081255
Chironomidae larvae        -0.197770967 -1.09115807
Cumella limicola            0.837578808  0.52899128
Cumella pygmaea            -0.166191910 -0.49815395
Cytharella costulata        0.040436547 -0.89281552
Diogenes pugilator          1.662949186 -1.44027806
Eteone flava                0.150083881  0.72788939
Eunice vittata              0.260840174  0.52434590
Eurydice dollfusi           1.231698114 -0.27754535
Exogone naidina            -2.298910099  0.22990753
Gastrosaccus sanctus        0.387692365  0.84749909
Genetyllis tuberculata     -0.182311804 -0.40163810
Glycera sp.                 0.238527682 -0.13812350
Glycera tridactyla         -0.469155135  0.47080089
Glycera unicornis           0.544276861  1.34868118
Harmothoe imbricata         0.288224431 -2.28020254
Harmothoe reticulata        1.206081486 -0.48921610
Heteromastus filiformis     1.296987623  0.68041424
Hirudinea                   0.842573600 -1.86388813
Hydrobia acuta             -0.525476356  0.84119437
Hydrobia sp.               -1.870674174 -0.49289037
Iphinoe tenella             0.978810388 -0.22037540
Kellia suborbicularis       0.638185344  1.02742536
Lagis koreni                1.940223417  0.29310519
Leiochone leiopygos         0.630744561  1.10132066
Lentidium mediterraneum    -0.339921638 -1.20931724
Lepidochitona cinerea      -0.002231745 -0.05112444
Loripes orbiculatus         0.996588429 -0.13778337
Lucinella divaricata       -0.362655475 -0.62076791
Magelona papillicornis      0.631025566  2.21308555
Maldane glebifex            1.510811164 -0.61554130
Melinna palmata             1.524144158 -0.50190005
Microdeutopus gryllotalpa   1.731022923 -0.36193193
Micromaldane ornithochaeta  0.418686662 -0.17446177
Micronephthys stammeri      1.292467568 -0.99639061
Microphthalmus fragilis    -0.238207804 -3.49575383
Microphthalmus sp.         -0.581858964 -0.98985479
Monocorophium acherusicum   1.056394357 -1.42893677
Mytilaster lineatus         1.502313325 -0.29264260
Mytilus galloprovincialis   0.224285931 -0.14420054
Nemertea                    2.100780277  0.04451835
Nephtys cirrosa             0.882747604  0.26596321
Nephtys kersivalensis      -0.542445996 -0.76263349
Nereis perivisceralis       0.835726966  2.04241087
Nereis pulsatoria           0.464742015  0.22189388
Nototropis guttatus         0.799764547  1.40849471
Oligochaeta                 0.311433818 -1.11395943
Paradoneis harpagonea       1.391451015  1.63431779
Parthenina interstincta    -0.126967379 -0.12786202
Parvicardium exiguum        1.519866294 -0.03013348
Perinereis cultrifera      -0.054229264 -1.50571985
Perioculodes longimanus     0.657582158 -0.84741762
Phoronida                   0.975844104 -1.33286091
Phyllodoce sp.             -0.338039801  0.24770039
Platyhelminthes            -0.017730472 -0.43180585
Platynereis dumerilii       1.060335167 -1.09722980
Polititapes aureus          2.092245769  0.83279777
Polychaeta larvae           1.323481602  1.10565396
Polydora ciliata            1.829791580 -1.05162540
Polygordius neapolitanus    0.256242551  1.15792022
Prionospio cirrifera        0.912871835 -0.51879750
Protodorvillea kefersteini -0.795002922 -0.32016043
Pseudocuma longicorne       0.729013541 -1.10140691
Rissoa membranacea          2.312290185  0.94287188
Rissoa splendida            0.112959686 -0.71515020
Salvatoria clavata          1.770682170 -0.94909715
Schistomeringos rudolphi    0.601123224  0.28528790
Sphaerosyllis hystrix       0.002225423  1.09909300
Spio filicornis             0.920675899  0.34609942
Spisula subtruncata         2.131600137 -0.08218578
Stenosoma capito           -0.419009313 -0.51613700
Syllis gracilis            -0.933227218 -1.16620835
Syllis hyalina              0.046552064  1.60408560
Tellina tenuis             -0.835424039  0.01540871
Thracia phaseolina          0.611076602  0.68992007
Tricolia pullus            -0.876044814  0.81014737
Tritia neritea             -0.608231361  0.44573152
Tritia reticulata           2.574671896 -1.17307789
Turbellaria                 1.983974647 -0.55700064
Upogebia pusilla           -2.078869648  1.07465115

$geweke.diag$geweke.diag$row.coefs
$geweke.diag$geweke.diag$row.coefs[[1]]
row.coefs.ID1[1] row.coefs.ID1[2] row.coefs.ID1[3] row.coefs.ID1[4] row.coefs.ID1[5] 
       -1.576104        -1.549594        -1.194765        -1.696688        -1.533687 



$geweke.diag$prop.exceed

     FALSE       TRUE 
0.93264249 0.06735751 


$family
 [1] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
 [5] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
 [9] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[13] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[17] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[21] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[25] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[29] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[33] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[37] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[41] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[45] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[49] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[53] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[57] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[61] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[65] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[69] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[73] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[77] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[81] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[85] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[89] "negative.binomial" "negative.binomial" "negative.binomial" "negative.binomial"
[93] "negative.binomial" "negative.binomial"

$num.lv
[1] 2

$lv.control
$lv.control$num.lv
[1] 2

$lv.control$type
[1] "independent"


$num.X
[1] 0

$num.traits
[1] 0

$calc.ics
[1] FALSE

$trial.size
 [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[43] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[85] 0 0 0 0 0 0 0 0 0 0

$prior.control
$prior.control$type
[1] "normal"  "normal"  "normal"  "uniform"

$prior.control$hypparams
[1] 10 10 10 30

$prior.control$ssvs.index
[1] -1

$prior.control$ssvs.g
[1] 1e-06

$prior.control$ssvs.traitsindex
[1] -1


$num.ord.levels
[1] 0

$mcmc.control
$mcmc.control$n.burnin
[1] 10000

$mcmc.control$n.iteration
[1] 40000

$mcmc.control$n.thin
[1] 30

$mcmc.control$seed
[1] 123


$format
[1] FALSE

attr(,"class")
[1] "boral"

Check the summary and diagnostic plots for the LVM.

summary(lvm.zostera)
$call
boral.default(y = zoo.abnd.flt.zostera, family = "negative.binomial", 
    lv.control = list(num.lv = 2), row.eff = "fixed", row.ids = matrix(rep(1:5, 
        times = c(8, 8, 4, 8, 4)), ncol = 1))

$coefficients
                            coefficients
cols                          beta0 theta1 theta2 Dispersion
  Abra alba                   2.198  1.988  0.000      0.805
  Abra sp.                   -1.608  1.860  0.689     20.217
  Actiniaria                 -2.575  1.839 -0.433     16.301
  Alitta succinea             1.287  2.962 -0.273      5.909
  Ampelisca diadema           3.916  0.203 -2.458      1.892
  Amphibalanus improvisus     1.243  2.972  0.827      1.134
  Ampithoe sp.                0.444  0.910 -1.998     10.014
  Anadara kagoshimensis      -2.476  1.031  2.128     15.707
  Apherusa bispinosa         -2.428 -1.186  0.307     15.831
  Apseudopsis ostroumovi      0.521 -5.653 -2.381      2.029
  Bittium reticulatum         5.338 -2.188  2.471      0.846
  Brachynotus sexdentatus    -1.433  0.672 -0.198     14.885
  Capitella capitata          1.076 -5.388 -0.928      1.170
  Capitella minima            4.479  0.928 -2.812      0.826
  Chamelea gallina           -0.328 -3.872  0.432      0.531
  Chironomidae larvae        -2.276 -2.524 -2.237     11.821
  Cumella limicola            0.896 -4.777 -0.004      0.436
  Cumella pygmaea            -1.927 -2.436  1.321     12.821
  Cytharella costulata       -0.069 -0.433 -0.632      1.365
  Diogenes pugilator         -0.177  0.968 -2.015      0.423
  Eteone flava               -2.885  1.639 -2.341     15.594
  Eunice vittata             -0.779  1.005 -1.601     16.372
  Eurydice dollfusi          -1.465 -2.009  0.879     15.626
  Exogone naidina            -0.462  0.723 -3.254     15.923
  Gastrosaccus sanctus       -2.368 -1.360  0.508     16.826
  Genetyllis tuberculata      0.293  0.005  0.259     10.334
  Glycera sp.                -0.740  2.095  0.024      5.525
  Glycera tridactyla         -1.041  1.003  2.501     12.689
  Glycera unicornis          -2.427  0.849  1.844     15.824
  Harmothoe imbricata        -0.653  0.192  3.196      5.920
  Harmothoe reticulata        0.462  0.415 -0.247      0.958
  Heteromastus filiformis     3.945  0.050  0.370      0.625
  Hirudinea                  -1.133  0.183  0.720     11.083
  Hydrobia acuta             -1.418  2.778 -0.307     21.032
  Hydrobia sp.               -0.577  2.065 -0.426     18.168
  Iphinoe tenella             0.352 -0.093  0.673      6.859
  Kellia suborbicularis      -0.363 -3.112  4.065      3.194
  Lagis koreni                1.062 -0.469  3.133      0.278
  Leiochone leiopygos         0.318 -1.764  3.210      0.498
  Lentidium mediterraneum    -2.097 -2.122  0.080     11.619
  Lepidochitona cinerea      -2.443 -1.418  0.273     15.545
  Loripes orbiculatus         1.922 -2.101  0.408      0.397
  Lucinella divaricata       -1.086 -2.794  0.848     19.669
  Magelona papillicornis     -2.592 -1.498 -0.331     16.872
  Maldane glebifex           -2.507  1.761 -0.177     16.326
  Melinna palmata             0.652  2.694 -1.236      2.709
  Microdeutopus gryllotalpa   1.941  0.402 -2.480      0.546
  Micromaldane ornithochaeta -0.860 -0.847 -1.357     15.169
  Micronephthys stammeri     -1.681  0.374 -1.377     15.521
  Microphthalmus fragilis    -1.199 -0.311  2.808     21.538
  Microphthalmus sp.         -1.678 -4.063 -2.984      5.775
  Monocorophium acherusicum   2.036  2.349 -3.210      1.058
  Mytilaster lineatus         3.458 -2.877 -0.639      1.990
  Mytilus galloprovincialis  -2.440  1.172  2.084     16.400
  Nemertea                    1.885 -0.349  1.128      0.641
  Nephtys cirrosa            -1.858 -1.029  1.939     11.741
  Nephtys kersivalensis      -2.406  0.799  2.018     15.678
  Nereis perivisceralis      -2.437 -1.341  0.676     16.179
  Nereis pulsatoria          -0.673  2.933  1.366     20.309
  Nototropis guttatus         0.552  0.331 -1.833      6.902
  Oligochaeta                 4.784 -1.839  0.190      1.090
  Paradoneis harpagonea      -2.676  2.076 -0.391     15.422
  Parthenina interstincta    -0.088  0.859  3.071     13.948
  Parvicardium exiguum        2.387  0.840 -0.939      1.586
  Perinereis cultrifera       0.507 -0.113 -1.661      6.654
  Perioculodes longimanus    -0.355  1.073 -2.670      1.471
  Phoronida                   0.418 -0.105  0.769      0.983
  Phyllodoce sp.             -3.020  1.597 -2.444     13.608
  Platyhelminthes             0.136  2.049  1.017      5.268
  Platynereis dumerilii       1.160  0.818 -3.257      0.534
  Polititapes aureus         -0.311 -0.003  0.208      8.166
  Polychaeta larvae          -2.476  1.324 -2.128     17.367
  Polydora ciliata            3.321  2.466 -0.944      3.736
  Polygordius neapolitanus   -2.562  1.460 -2.102     16.578
  Prionospio cirrifera        3.661  1.111 -0.632      3.972
  Protodorvillea kefersteini  1.712 -2.163  0.213      2.182
  Pseudocuma longicorne      -1.187  0.060 -0.649     12.114
  Rissoa membranacea          3.074  0.352 -1.468      1.252
  Rissoa splendida           -1.177 -1.453 -3.972      2.213
  Salvatoria clavata         -1.107 -2.064 -4.812      0.653
  Schistomeringos rudolphi    0.407 -1.532  4.380      5.729
  Sphaerosyllis hystrix      -0.252 -3.320  0.508      0.732
  Spio filicornis             1.884  2.108 -2.790      3.201
  Spisula subtruncata        -1.821 -2.397 -0.363      6.609
  Stenosoma capito            1.030 -1.190 -1.260      2.092
  Syllis gracilis             1.417 -2.385  0.383      2.745
  Syllis hyalina             -1.882 -2.749 -2.334     19.788
  Tellina tenuis             -1.540 -1.725  1.252      8.397
  Thracia phaseolina         -2.348 -1.154  0.295     15.251
  Tricolia pullus            -1.550 -3.068 -2.264      1.143
  Tritia neritea             -0.969  1.676 -1.193     14.442
  Tritia reticulata           0.147  0.035  1.052      5.493
  Turbellaria                 0.393  0.927 -0.384     14.925
  Upogebia pusilla           -2.292 -2.751 -2.773     12.546

$lvs
    lv
rows    lv1    lv2
  1   0.633 -0.251
  2   0.719 -0.167
  3   0.561 -0.427
  4   0.552 -0.125
  5   0.310  0.418
  6   0.247  0.446
  7   0.329  0.500
  8   0.410  0.269
  9   0.344 -0.052
  10  0.306  0.058
  11 -0.033 -0.311
  12  0.335  0.063
  13 -0.032  0.438
  14  0.220  0.338
  15  0.073  0.375
  16 -0.139  0.245
  17  0.339 -0.806
  18  0.409 -0.803
  19  0.595 -1.032
  20  0.430 -1.046
  21 -0.544 -0.201
  22 -0.397  0.003
  23 -0.412 -0.046
  24 -0.254  0.022
  25 -0.341 -0.059
  26 -0.433  0.069
  27 -0.508  0.140
  28 -0.513  0.142
  29 -0.474 -0.627
  30 -0.555 -0.633
  31 -0.342 -0.333
  32 -0.474 -0.433

$row.coefficients
$row.coefficients[[1]]
     1      2      3      4      5 
-1.561 -0.963 -2.739 -0.965 -1.000 


$est
[1] "median"

$calc.ics
[1] FALSE

$trial.size
 [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[43] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[85] 0 0 0 0 0 0 0 0 0 0

$num.ord.levels
[1] 0

$prior.control
$prior.control$ssvs.index
[1] -1


attr(,"class")
[1] "summary.boral"
## model fit diagnostic plots
plot(lvm.zostera) 
NULL

The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a (more or less) normal distribution of the residuals) - the model fits the data pretty well.

Save the zostera LVM.

write_rds(lvm.zostera, 
          here(save.dir, "lvm_zostera.RDS"))

Save the diagnostic plots.

png(here(figures.dir, "diagnostic_lvm_zostera.png"), width = 25, height = 20, units = "cm", res = 300)
par(mfrow = c(2, 2))
plot(lvm.zostera)
NULL
par(mfrow = c(1, 1))
dev.off()
null device 
          1 

Examine the biplot obtained by fitting the LVM, as well as the 20 most “important” species.

lvsplot(lvm.zostera, jitter = T, biplot = TRUE, ind.spp = 20)
Only the first 20 ``most important'' latent variable coefficients included in biplot

All in all, the final result resembles the nMDS ordination very much - same stretched clusters (Poda + Otmanli, Vromos pretty much apart, Gradina +- Ropotamo). I don’t see much difference with the nMDS. The main difference seems to be the distance between the 2 years for Poda ana Otmanli - the LVM enlarges it. Have to remember to test for year effect! The run time is actually not that bad for the seagrasses. The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I’m not adding the species on top, first because I’m too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.

## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.zostera <- as_tibble(lvm.zostera$lv.median)
## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.zostera <- lvs.coord.zostera %>% 
  bind_cols(zoo.abnd.zostera %>% select(station))
)

Make the plot and save it.

(plot.lvm.zostera <- ggplot(lvs.coord.zostera) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("Z", as.numeric((unique(lvs.coord.zostera %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

Well, this is a weird one - this plot is flipped around 0 compared to the one that boral’s plotting function gives. Otherwise nothing changes - the spatial relationships between samples are preserved. I suppose it doesn’t matter much - the axes are arbitrary after all, but strange that it happens.

## save the LVM plot for the seagrass
ggsave(file = here(figures.dir, "lvm_zostera.png"), 
       plot.lvm.zostera, 
       width = 15, height = 10, units = "cm", dpi = 300)
GLM fitting for abundance - environmental data

Fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.
These functions all come from package mvabund.
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (as long-term as available, at least) at each station, repeated for each replicate, the sediment data (2013-2014), and the seagrass data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.

env.zostera <- read_csv(here(save.dir, "env_data_ordinations_zostera.csv"))

## convert station to factor
(env.zostera <- env.zostera %>% 
    mutate(station = factor(station,
                            levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)

Station is a factor, the rest of the variables are numeric.

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.

## there is already one subset of filtered count data (32 x 94) - use it 
zoo.mvabnd.zostera <- mvabund(zoo.abnd.flt.zostera)
manyGLM by LVM clusters

First, let’s see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.
I’m going to try something new here - 1) loose clusters from the LVM ordination, 1 = Poda-Otmanli, 2 = Vromos, 3 = Gradina-Ropotamo. 2) stations as clusters, as I did before for the seagrass data, although I don’t believe it’s valid/justified to do so… 3) another possible configuration of clusters from the LVM ordination: 1 = Z1-Z2, 2 = Z3, 3 = Z4, 4 = Z5.

## construct the vectors of the clusters by hand - first, situation 1 above
lvm.clusters.zostera.1 <- rep(1:3, times = c(16, 4, 12))
(lvm.clusters.zostera.1 <- factor(lvm.clusters.zostera.1))

## again, for case 2
lvm.clusters.zostera.2 <- rep(1:5, times = c(8, 8, 4, 8, 4))
(lvm.clusters.zostera.2 <- factor(lvm.clusters.zostera.2))

## again, for case 3
lvm.clusters.zostera.3 <- rep(1:4, times = c(16, 4, 8, 4))
(lvm.clusters.zostera.3 <- factor(lvm.clusters.zostera.3))

LVM clusters - case 1 Check the model assumptions. 1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.
Another way: direct plotting (variance ~ mean), for each species within each factor level.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, table = TRUE)

It’s not perfect, but it’s not too terrible either.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula. When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.1 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.1)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.1, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

I really don’t like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.
Save the model!

write_rds(glms.lvm.zostera.1, 
          here(save.dir, "glms_lvm_zostera_1.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.zostera.1.summary <- summary(glms.lvm.zostera.1, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)

The factor is highly significant according to the models.
This also allows us to see which species exhibit a response to the chosen factor. The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. I’ll save the summary for safekeeping, but I’ll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).

write_rds(glms.lvm.zostera.1.summary, 
          here(save.dir, "glms_lvm_zostera_1_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.1.aov <- anova.manyglm(glms.lvm.zostera.1, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time
                                    pairwise.comp = ~lvm.clusters.zostera.1, ## check the pairwise comparison between clusters
                                    show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.25 minutes...
    Resampling run 300 finished. Time elapsed: 0.38 minutes...
    Resampling run 400 finished. Time elapsed: 0.50 minutes...
    Resampling run 500 finished. Time elapsed: 0.63 minutes...
    Resampling run 600 finished. Time elapsed: 0.75 minutes...
    Resampling run 700 finished. Time elapsed: 0.88 minutes...
    Resampling run 800 finished. Time elapsed: 1.01 minutes...
    Resampling run 900 finished. Time elapsed: 1.13 minutes...
Time elapsed: 0 hr 1 min 14 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff   Dev Pr(>Dev)    
(Intercept)                31                           
lvm.clusters.zostera.1     29       2 703.6    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Pairwise comparison results: 
                                                     Observed statistic
lvm.clusters.zostera.1:1 vs lvm.clusters.zostera.1:3              370.0
lvm.clusters.zostera.1:2 vs lvm.clusters.zostera.1:3              346.1
lvm.clusters.zostera.1:1 vs lvm.clusters.zostera.1:2              319.4
                                                     Free Stepdown Adjusted P-Value    
lvm.clusters.zostera.1:1 vs lvm.clusters.zostera.1:3                          0.001 ***
lvm.clusters.zostera.1:2 vs lvm.clusters.zostera.1:3                          0.001 ***
lvm.clusters.zostera.1:1 vs lvm.clusters.zostera.1:2                          0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.1    25.931    0.002    4.159    0.986      1.386    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1           8.646    0.434            20.059    0.005
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1                  14.882    0.036        6.321    0.802
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.1                 1.386    1.000              1.962    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1                 30.855    0.001              31.183    0.001
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1                   0.575    1.000             26.213    0.002
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1            0.739    1.000            26.23    0.002
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1               4.195    0.979           32.545    0.001
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1           4.228    0.979                3.122    0.996
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.1              0.896    1.000        4.159    0.987          0.871
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1    1.000             4.228    0.979           5.944    0.839
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1                1.962    1.000                  0.467    1.000
                       Glycera.sp.          Glycera.tridactyla         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.1       7.992    0.559              4.484    0.961
                       Glycera.unicornis          Harmothoe.imbricata         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1             1.386    1.000               1.841    1.000
                       Harmothoe.reticulata          Heteromastus.filiformis         
                                        Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.1                 5.13    0.925                  10.222    0.247
                       Hirudinea          Hydrobia.acuta          Hydrobia.sp.         
                             Dev Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                            
lvm.clusters.zostera.1     0.915    1.000          1.438    1.000        1.681    1.000
                       Iphinoe.tenella          Kellia.suborbicularis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1            4.16    0.981                 4.584    0.949
                       Lagis.koreni          Leiochone.leiopygos         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.1        9.705    0.296               6.218    0.812
                       Lentidium.mediterraneum          Lepidochitona.cinerea         
                                           Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.1                   3.923    0.989                 1.962    1.000
                       Loripes.orbiculatus          Lucinella.divaricata         
                                       Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.1              25.259    0.002                4.257    0.979
                       Magelona.papillicornis          Maldane.glebifex         
                                          Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.1                  1.962    1.000            1.386    1.000
                       Melinna.palmata          Microdeutopus.gryllotalpa         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.1          24.203    0.003                     3.088    0.996
                       Micromaldane.ornithochaeta          Micronephthys.stammeri
                                              Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
lvm.clusters.zostera.1                      4.544    0.959                  0.575
                                Microphthalmus.fragilis          Microphthalmus.sp.
                       Pr(>Dev)                     Dev Pr(>Dev)                Dev
(Intercept)                                                                        
lvm.clusters.zostera.1    1.000                   1.437    1.000              9.396
                                Monocorophium.acherusicum          Mytilaster.lineatus
                       Pr(>Dev)                       Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
lvm.clusters.zostera.1    0.342                    38.329    0.001              21.933
                                Mytilus.galloprovincialis          Nemertea         
                       Pr(>Dev)                       Dev Pr(>Dev)      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1    0.003                     1.386    1.000    3.554    0.995
                       Nephtys.cirrosa          Nephtys.kersivalensis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1           0.575    1.000                 1.386    1.000
                       Nereis.perivisceralis          Nereis.pulsatoria         
                                         Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.1                 1.962    1.000             2.987    0.998
                       Nototropis.guttatus          Oligochaeta         
                                       Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                             
lvm.clusters.zostera.1                2.61    0.999      21.776    0.003
                       Paradoneis.harpagonea          Parthenina.interstincta         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.1                 1.386    1.000                   1.965    1.000
                       Parvicardium.exiguum          Perinereis.cultrifera         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1                2.086    1.000                  3.68    0.995
                       Perioculodes.longimanus          Phoronida         
                                           Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1                   2.254    0.999     4.088    0.989
                       Phyllodoce.sp.          Platyhelminthes         
                                  Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.1          4.159    0.987           4.534    0.959
                       Platynereis.dumerilii          Polititapes.aureus         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.1                  7.28    0.627              3.315    0.996
                       Polychaeta.larvae          Polydora.ciliata         
                                     Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                
lvm.clusters.zostera.1             4.159    0.984            15.69    0.022
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.1                    4.159    0.984               13.193    0.072
                       Protodorvillea.kefersteini          Pseudocuma.longicorne
                                              Dev Pr(>Dev)                   Dev
(Intercept)                                                                     
lvm.clusters.zostera.1                     17.536    0.009                 1.491
                                Rissoa.membranacea          Rissoa.splendida         
                       Pr(>Dev)                Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.1    1.000              0.158    1.000           11.549    0.145
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1             17.003    0.015                    2.634    0.999
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1                12.713    0.085          28.109    0.001
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1               5.885    0.842            5.011    0.930
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                                                                           
lvm.clusters.zostera.1           5.956    0.839          2.048    1.000          1.491
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1    1.000              1.962    1.000           7.956    0.559
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                          
lvm.clusters.zostera.1          1.406    1.000             2.932    0.999       0.135
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                              
lvm.clusters.zostera.1    1.000            4.257    0.979
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Aaaand the differences between clusters are highly significant in this iteration..

Save the ANOVA, too.

write_rds(glms.lvm.zostera.1.aov, 
          here(save.dir, "glms_lvm_zostera_1_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.1 <- top_n_sp_glm(glms.lvm.zostera.1.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.76"
 Monocorophium.acherusicum           Cumella.limicola        Bittium.reticulatum 
                 38.328670                  32.545296                  31.182981 
    Apseudopsis.ostroumovi            Spio.filicornis           Chamelea.gallina 
                 30.854772                  28.108956                  26.230014 
        Capitella.capitata                  Abra.alba        Loripes.orbiculatus 
                 26.212753                  25.931365                  25.258931 
           Melinna.palmata        Mytilaster.lineatus                Oligochaeta 
                 24.202974                  21.932810                  21.776133 
         Ampelisca.diadema Protodorvillea.kefersteini         Salvatoria.clavata 
                 20.058951                  17.536359                  17.003452 
          Polydora.ciliata    Amphibalanus.improvisus       Prionospio.cirrifera 
                 15.689516                  14.882244                  13.192537 
     Sphaerosyllis.hystrix           Rissoa.splendida    Heteromastus.filiformis 
                 12.713470                  11.548802                  10.221754 
              Lagis.koreni         Microphthalmus.sp.            Alitta.succinea 
                  9.704792                   9.395618                   8.646146 
               Glycera.sp.            Tricolia.pullus      Platynereis.dumerilii 
                  7.992056                   7.955930                   7.279560 
              Ampithoe.sp.        Leiochone.leiopygos            Syllis.gracilis 
                  6.321173                   6.218039                   5.956444 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.1) <- names(top.sp.glms.lvm.zostera.1) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.1
 Monocorophium acherusicum           Cumella limicola        Bittium reticulatum 
                 38.328670                  32.545296                  31.182981 
    Apseudopsis ostroumovi            Spio filicornis           Chamelea gallina 
                 30.854772                  28.108956                  26.230014 
        Capitella capitata                  Abra alba        Loripes orbiculatus 
                 26.212753                  25.931365                  25.258931 
           Melinna palmata        Mytilaster lineatus                Oligochaeta 
                 24.202974                  21.932810                  21.776133 
         Ampelisca diadema Protodorvillea kefersteini         Salvatoria clavata 
                 20.058951                  17.536359                  17.003452 
          Polydora ciliata    Amphibalanus improvisus       Prionospio cirrifera 
                 15.689516                  14.882244                  13.192537 
     Sphaerosyllis hystrix           Rissoa splendida    Heteromastus filiformis 
                 12.713470                  11.548802                  10.221754 
              Lagis koreni         Microphthalmus sp.            Alitta succinea 
                  9.704792                   9.395618                   8.646146 
               Glycera sp.            Tricolia pullus      Platynereis dumerilii 
                  7.992056                   7.955930                   7.279560 
              Ampithoe sp.        Leiochone leiopygos            Syllis gracilis 
                  6.321173                   6.218039                   5.956444 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.1 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.1)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.1)))) %>% 
   mutate(group = factor(case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                                   station == "Vromos" ~ 2, 
                                   station %in% c("Gradina", "Ropotamo") ~ 3))) ## add the groups to the long df 
)
(plot.top.sp.glms.lvm.zostera.1 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.1,
                                         mapping = aes(x = species, y = log_y_min(count), colour = group),
                                         labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.1$group))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())
)

Well this is a nightmarish plot, but more tolerable than the one for the sand stations - there are less species here, so at least it’s readable..

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.1 <- lapply(names(glms.lvm.zostera.1.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.1.summary, x, p = 0.05)) 
## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))
## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.1")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.1", "group_"))))
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))
## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.1 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                           station == "Vromos" ~ 2, 
                           station %in% c("Gradina", "Ropotamo") ~ 3)
         )
## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.1.smry <- zoo.abnd.zostera.long.1 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()
## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, zoo.abnd.zostera.long.1.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.1.smry %>% filter(group == .y) %>% unnest(), by = "species"))
## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, c(16, 4, 12), function(x, y) x %>% mutate(mean_count = total_count/y))
)
[[1]]

[[2]]

[[3]]
NA

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.
I have to say, in the case of the seagrasses and case 1 clusters, there are much fewer species that exhibit a significant response - around 10 for each group.
The LRs are lower for groups 2 and 3 - not sure if this means anything, but for group 1 they are much much higher..
For group 1 (= Z1-Z2), the species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Oligochaeta, H. filiformis, Polydora ciliata, Prionospio cirrifera, R. membranacea, A. alba, A.diadema, M. acherusicum; and the only one with a significantly lower abundance - Chamelea gallina.
For group 2 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A.dadema. The species with lower abundance are: B. reticulatum, A. alba, Oligochaeta, S. clavata, P. ciliata, P. cirrifera, H. filiformis.
For group 3 (= Z4-Z5), the species with higher abundance are: Cumella limicola, Apseudopsis ostroumovi, Capitella capitata, Mytilaster lineatus, Loripes orbiculatus; less so, but still present - C. gallina, S. clavata. The species with lower abundance are: Abra alba, Melinna palmata (totally absent).

I’ll test each station as its own group, too (as I did before, with the classical multivariate methods) - I’m not sure how much I can trust this grouping (in particular group 3 is a bit far-fetched, if you ask me..).

LVM clusters - case 2 Check the model assumptions.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, table = TRUE)

It’s not perfect, but it’s not too terrible either. I think it’s a little worse than the case 1 fit.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.2 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.2)


## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.2, which = 1:3)

Save the model!

write_rds(glms.lvm.zostera.2, 
          here(save.dir, "glms_lvm_zostera_2.RDS"))

Save the model diagnostic plots - only for this one, since - spoiler alert! - I’m going with it in the end; it’s marginally better than the other two options.

png(here(figures.dir, "diagnostic_glms_lvm_zostera_2.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(glms.lvm.zostera.2, which = 1:3)
dev.off()
null device 
          1 

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

glms.lvm.zostera.2.summary

Test statistics:
                        LR value Pr(>LR)    
(Intercept)               1080.0   0.001 ***
lvm.clusters.zostera.22    256.8   0.001 ***
lvm.clusters.zostera.23    310.9   0.001 ***
lvm.clusters.zostera.24    471.9   0.001 ***
lvm.clusters.zostera.25    346.6   0.001 ***
--- 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Univariate test statistic: 
                           (Intercept)         lvm.clusters.zostera.22        
                              LR value Pr(>LR)                LR value Pr(>LR)
Abra.alba                       31.096   0.001                   0.023   1.000
Abra.sp.                         4.677   0.714                   0.000   1.000
Actiniaria                       2.341   0.978                   1.386   0.990
Alitta.succinea                 25.658   0.001                  23.057   0.002
Ampelisca.diadema               54.649   0.001                  10.416   0.072
Amphibalanus.improvisus         23.546   0.001                   8.177   0.181
Ampithoe.sp.                     8.217   0.202                   3.482   0.823
Anadara.kagoshimensis            2.341   0.978                   1.386   0.990
Apherusa.bispinosa               3.770   0.854                   0.000   1.000
Apseudopsis.ostroumovi          14.963   0.013                   1.380   0.992
Bittium.reticulatum            126.101   0.001                   0.004   1.000
Brachynotus.sexdentatus          3.387   0.910                   1.386   0.990
Capitella.capitata               5.997   0.502                   2.862   0.912
Capitella.minima               132.041   0.001                   0.433   1.000
Chamelea.gallina                15.617   0.009                   1.386   0.990
Chironomidae.larvae              6.560   0.425                   0.000   1.000
Cumella.limicola                13.674   0.027                   7.694   0.208
Cumella.pygmaea                  5.165   0.620                   0.000   1.000
Cytharella.costulata            12.759   0.036                   4.159   0.675
Diogenes.pugilator               6.380   0.439                   0.680   0.999
Eteone.flava                     4.677   0.714                   0.000   1.000
Eunice.vittata                   1.521   0.992                   0.208   1.000
Eurydice.dollfusi                5.165   0.620                   0.000   1.000
Exogone.naidina                  5.874   0.506                   1.250   0.995
Gastrosaccus.sanctus             3.770   0.854                   0.000   1.000
Genetyllis.tuberculata           6.742   0.398                   5.746   0.444
Glycera.sp.                      2.965   0.944                   0.000   1.000
Glycera.tridactyla               2.776   0.955                   1.033   0.998
Glycera.unicornis                2.341   0.978                   1.386   0.990
Harmothoe.imbricata              0.759   1.000                   5.561   0.476
Harmothoe.reticulata             6.385   0.439                   5.794   0.444
Heteromastus.filiformis         62.249   0.001                  10.679   0.060
Hirudinea                        4.137   0.812                   0.000   1.000
Hydrobia.acuta                   0.171   1.000                   1.494   0.983
Hydrobia.sp.                     0.116   1.000                   3.709   0.788
Iphinoe.tenella                  4.775   0.705                   4.354   0.646
Kellia.suborbicularis            1.985   0.978                   0.104   1.000
Lagis.koreni                     0.095   1.000                   5.999   0.421
Leiochone.leiopygos              1.899   0.978                   0.336   1.000
Lentidium.mediterraneum          6.813   0.388                   0.000   1.000
Lepidochitona.cinerea            3.770   0.854                   0.000   1.000
Loripes.orbiculatus              1.160   0.995                   3.172   0.869
Lucinella.divaricata             3.682   0.861                   0.000   1.000
Magelona.papillicornis           3.770   0.854                   0.000   1.000
Maldane.glebifex                 2.341   0.978                   1.386   0.990
Melinna.palmata                  2.455   0.978                   2.657   0.931
Microdeutopus.gryllotalpa       14.797   0.013                   2.603   0.933
Micromaldane.ornithochaeta       6.542   0.426                   0.000   1.000
Micronephthys.stammeri           3.925   0.837                   1.386   0.990
Microphthalmus.fragilis          1.716   0.983                   1.494   0.983
Microphthalmus.sp.               5.680   0.536                   0.000   1.000
Monocorophium.acherusicum       12.799   0.036                   0.213   1.000
Mytilaster.lineatus              0.385   1.000                  12.953   0.032
Mytilus.galloprovincialis        2.341   0.978                   1.386   0.990
Nemertea                         0.000   1.000                   5.479   0.494
Nephtys.cirrosa                  5.423   0.582                   1.386   0.990
Nephtys.kersivalensis            2.341   0.978                   1.386   0.990
Nereis.perivisceralis            3.770   0.854                   0.000   1.000
Nereis.pulsatoria                0.020   1.000                   3.251   0.853
Nototropis.guttatus              0.402   1.000                   0.116   1.000
Oligochaeta                     58.093   0.001                   9.386   0.110
Paradoneis.harpagonea            2.341   0.978                   1.386   0.990
Parthenina.interstincta          0.017   1.000                   1.662   0.983
Parvicardium.exiguum             6.468   0.429                   0.063   1.000
Perinereis.cultrifera            0.177   1.000                   2.035   0.967
Perioculodes.longimanus          2.180   0.978                   0.000   1.000
Phoronida                        2.237   0.978                   0.110   1.000
Phyllodoce.sp.                   4.677   0.714                   0.000   1.000
Platyhelminthes                  0.058   1.000                   2.602   0.933
Platynereis.dumerilii            1.999   0.978                   0.374   1.000
Polititapes.aureus               9.599   0.112                   6.933   0.288
Polychaeta.larvae                4.677   0.714                   0.000   1.000
Polydora.ciliata                91.477   0.001                  12.416   0.033
Polygordius.neapolitanus         4.677   0.714                   0.000   1.000
Prionospio.cirrifera            49.773   0.001                   4.922   0.568
Protodorvillea.kefersteini       5.371   0.585                   4.879   0.568
Pseudocuma.longicorne            4.585   0.729                   1.386   0.990
Rissoa.membranacea              20.908   0.001                   1.019   0.998
Rissoa.splendida                10.372   0.071                   0.000   1.000
Salvatoria.clavata              14.727   0.013                   0.000   1.000
Schistomeringos.rudolphi         6.673   0.412                   8.799   0.141
Sphaerosyllis.hystrix           12.303   0.039                   4.024   0.720
Spio.filicornis                  0.320   1.000                   0.246   1.000
Spisula.subtruncata              8.280   0.194                   0.000   1.000
Stenosoma.capito                 3.207   0.929                   6.661   0.330
Syllis.gracilis                 11.730   0.042                  17.831   0.005
Syllis.hyalina                   2.396   0.978                   0.000   1.000
Tellina.tenuis                   7.750   0.294                   1.386   0.990
Thracia.phaseolina               3.770   0.854                   0.000   1.000
Tricolia.pullus                 11.452   0.047                   1.380   0.992
Tritia.neritea                   0.707   1.000                   3.479   0.823
Tritia.reticulata                9.399   0.132                   8.301   0.174
Turbellaria                      0.265   1.000                   1.125   0.998
Upogebia.pusilla                 5.886   0.505                   0.000   1.000
                           lvm.clusters.zostera.23         lvm.clusters.zostera.24
                                          LR value Pr(>LR)                LR value
Abra.alba                                   17.297   0.003                  13.450
Abra.sp.                                     2.197   0.783                   0.000
Actiniaria                                   0.811   0.947                   1.386
Alitta.succinea                             15.046   0.008                  23.057
Ampelisca.diadema                           12.759   0.014                   3.426
Amphibalanus.improvisus                     10.584   0.036                  16.614
Ampithoe.sp.                                 9.419   0.062                   4.372
Anadara.kagoshimensis                        0.811   0.947                   1.386
Apherusa.bispinosa                           0.000   1.000                   1.386
Apseudopsis.ostroumovi                       0.000   0.969                  26.746
Bittium.reticulatum                         24.917   0.001                   6.987
Brachynotus.sexdentatus                      0.811   0.947                   0.000
Capitella.capitata                           0.773   0.950                  17.684
Capitella.minima                             0.333   0.969                   2.753
Chamelea.gallina                             0.000   1.000                  19.316
Chironomidae.larvae                          0.000   0.969                   0.000
Cumella.limicola                             0.000   1.000                  31.096
Cumella.pygmaea                              0.000   1.000                   3.167
Cytharella.costulata                         2.197   0.783                   6.931
Diogenes.pugilator                           1.483   0.898                   0.000
Eteone.flava                                 2.197   0.783                   0.000
Eunice.vittata                               1.199   0.898                   2.081
Eurydice.dollfusi                            0.000   1.000                   3.167
Exogone.naidina                              6.160   0.228                   2.262
Gastrosaccus.sanctus                         0.000   1.000                   1.386
Genetyllis.tuberculata                       1.876   0.857                   3.160
Glycera.sp.                                  2.428   0.738                   4.124
Glycera.tridactyla                           0.718   0.958                   1.242
Glycera.unicornis                            0.811   0.947                   1.386
Harmothoe.imbricata                          3.293   0.613                   0.994
Harmothoe.reticulata                         1.622   0.893                   0.340
Heteromastus.filiformis                      7.032   0.170                   8.276
Hirudinea                                    0.811   0.947                   0.000
Hydrobia.acuta                               0.884   0.941                   1.494
Hydrobia.sp.                                 2.194   0.783                   1.407
Iphinoe.tenella                              0.762   0.952                   0.276
Kellia.suborbicularis                        1.257   0.898                   3.343
Lagis.koreni                                 4.950   0.375                   0.180
Leiochone.leiopygos                          3.040   0.670                   4.486
Lentidium.mediterraneum                      0.000   1.000                   2.773
Lepidochitona.cinerea                        0.000   1.000                   1.386
Loripes.orbiculatus                          0.068   0.969                  23.773
Lucinella.divaricata                         0.000   1.000                   3.204
Magelona.papillicornis                       0.000   1.000                   1.386
Maldane.glebifex                             0.811   0.947                   1.386
Melinna.palmata                              9.495   0.062                   5.545
Microdeutopus.gryllotalpa                    0.089   0.969                   1.848
Micromaldane.ornithochaeta                   2.067   0.809                   3.568
Micronephthys.stammeri                       0.811   0.947                   1.386
Microphthalmus.fragilis                      0.000   0.969                   0.000
Microphthalmus.sp.                           0.000   0.969                   3.972
Monocorophium.acherusicum                   20.414   0.002                   4.667
Mytilaster.lineatus                          2.713   0.724                  35.697
Mytilus.galloprovincialis                    0.811   0.947                   1.386
Nemertea                                     0.608   0.958                   4.090
Nephtys.cirrosa                              0.000   1.000                   1.386
Nephtys.kersivalensis                        0.811   0.947                   1.386
Nereis.perivisceralis                        0.000   1.000                   1.386
Nereis.pulsatoria                            1.949   0.850                   3.251
Nototropis.guttatus                          2.528   0.725                   1.537
Oligochaeta                                 11.422   0.027                   9.333
Paradoneis.harpagonea                        0.811   0.947                   1.386
Parthenina.interstincta                      2.228   0.775                   0.968
Parvicardium.exiguum                         1.435   0.898                   0.029
Perinereis.cultrifera                        2.924   0.685                   0.035
Perioculodes.longimanus                      1.591   0.898                   0.850
Phoronida                                    3.210   0.631                   0.396
Phyllodoce.sp.                               2.197   0.783                   0.000
Platyhelminthes                              4.577   0.403                   2.602
Platynereis.dumerilii                        4.688   0.403                   0.049
Polititapes.aureus                           0.000   1.000                   1.367
Polychaeta.larvae                            2.197   0.783                   0.000
Polydora.ciliata                            24.008   0.001                  30.614
Polygordius.neapolitanus                     2.197   0.783                   0.000
Prionospio.cirrifera                        18.028   0.002                  29.724
Protodorvillea.kefersteini                   1.584   0.898                  20.929
Pseudocuma.longicorne                        0.811   0.947                   0.000
Rissoa.membranacea                           0.725   0.958                   1.256
Rissoa.splendida                             7.113   0.167                   2.626
Salvatoria.clavata                          12.384   0.017                   4.104
Schistomeringos.rudolphi                     0.000   1.000                   6.233
Sphaerosyllis.hystrix                        0.000   0.969                  11.891
Spio.filicornis                             19.150   0.002                   0.000
Spisula.subtruncata                          0.000   0.975                   2.773
Stenosoma.capito                             1.424   0.898                   1.680
Syllis.gracilis                              0.000   1.000                   8.039
Syllis.hyalina                               0.000   0.969                   0.000
Tellina.tenuis                               0.000   1.000                   2.773
Thracia.phaseolina                           0.000   1.000                   1.386
Tricolia.pullus                              0.000   0.969                   2.745
Tritia.neritea                               2.051   0.812                   1.033
Tritia.reticulata                            0.000   0.969                   2.586
Turbellaria                                  0.285   0.969                   0.158
Upogebia.pusilla                             0.000   1.000                   0.000
                                   lvm.clusters.zostera.25        
                           Pr(>LR)                LR value Pr(>LR)
Abra.alba                    0.018                   4.346   0.669
Abra.sp.                     1.000                   0.000   1.000
Actiniaria                   0.996                   0.811   0.999
Alitta.succinea              0.002                   6.818   0.295
Ampelisca.diadema            0.806                   1.516   0.991
Amphibalanus.improvisus      0.005                   8.450   0.159
Ampithoe.sp.                 0.642                   0.000   1.000
Anadara.kagoshimensis        0.996                   0.811   0.999
Apherusa.bispinosa           0.995                   0.000   0.999
Apseudopsis.ostroumovi       0.001                  39.178   0.001
Bittium.reticulatum          0.249                   0.201   0.999
Brachynotus.sexdentatus      1.000                   0.811   0.999
Capitella.capitata           0.005                  22.609   0.001
Capitella.minima             0.934                   1.211   0.994
Chamelea.gallina             0.005                  10.986   0.050
Chironomidae.larvae          1.000                   5.456   0.476
Cumella.limicola             0.001                  26.312   0.001
Cumella.pygmaea              0.849                   0.000   1.000
Cytharella.costulata         0.256                   4.394   0.664
Diogenes.pugilator           1.000                   1.483   0.991
Eteone.flava                 1.000                   0.000   1.000
Eunice.vittata               0.983                   0.210   0.999
Eurydice.dollfusi            0.849                   0.000   0.999
Exogone.naidina              0.972                   0.000   0.999
Gastrosaccus.sanctus         0.996                   0.000   1.000
Genetyllis.tuberculata       0.850                   0.000   1.000
Glycera.sp.                  0.721                   2.428   0.938
Glycera.tridactyla           0.997                   0.718   0.999
Glycera.unicornis            0.996                   0.811   0.999
Harmothoe.imbricata          0.998                   3.293   0.805
Harmothoe.reticulata         1.000                   2.773   0.880
Heteromastus.filiformis      0.172                   1.330   0.994
Hirudinea                    1.000                   0.811   0.999
Hydrobia.acuta               0.993                   0.884   0.999
Hydrobia.sp.                 0.995                   2.194   0.953
Iphinoe.tenella              1.000                   0.762   0.999
Kellia.suborbicularis        0.818                   1.257   0.994
Lagis.koreni                 1.000                   0.420   0.999
Leiochone.leiopygos          0.624                   3.040   0.837
Lentidium.mediterraneum      0.921                   0.000   1.000
Lepidochitona.cinerea        0.995                   0.000   1.000
Loripes.orbiculatus          0.002                  12.893   0.023
Lucinella.divaricata         0.844                   0.000   1.000
Magelona.papillicornis       0.996                   0.000   1.000
Maldane.glebifex             0.996                   0.811   0.999
Melinna.palmata              0.470                   3.244   0.807
Microdeutopus.gryllotalpa    0.989                   6.470   0.331
Micromaldane.ornithochaeta   0.786                   0.000   1.000
Micronephthys.stammeri       0.995                   0.236   0.999
Microphthalmus.fragilis      1.000                   0.000   1.000
Microphthalmus.sp.           0.731                   7.235   0.253
Monocorophium.acherusicum    0.605                   0.479   0.999
Mytilaster.lineatus          0.001                   3.994   0.738
Mytilus.galloprovincialis    0.996                   0.811   0.999
Nemertea                     0.722                   0.324   0.999
Nephtys.cirrosa              0.995                   0.000   0.999
Nephtys.kersivalensis        0.996                   0.811   0.999
Nereis.perivisceralis        0.996                   0.000   1.000
Nereis.pulsatoria            0.831                   1.949   0.972
Nototropis.guttatus          0.992                   1.502   0.991
Oligochaeta                  0.100                  21.743   0.001
Paradoneis.harpagonea        0.996                   0.811   0.999
Parthenina.interstincta      0.998                   2.228   0.951
Parvicardium.exiguum         1.000                   0.610   0.999
Perinereis.cultrifera        1.000                   0.836   0.999
Perioculodes.longimanus      0.998                   0.467   0.999
Phoronida                    1.000                   0.433   0.999
Phyllodoce.sp.               1.000                   0.000   1.000
Platyhelminthes              0.954                   4.577   0.632
Platynereis.dumerilii        1.000                   0.899   0.999
Polititapes.aureus           0.996                   0.000   1.000
Polychaeta.larvae            1.000                   0.000   1.000
Polydora.ciliata             0.001                   5.015   0.546
Polygordius.neapolitanus     1.000                   0.000   1.000
Prionospio.cirrifera         0.001                   0.688   0.999
Protodorvillea.kefersteini   0.004                   3.630   0.780
Pseudocuma.longicorne        1.000                   0.236   0.999
Rissoa.membranacea           0.997                   0.171   0.999
Rissoa.splendida             0.950                  11.194   0.047
Salvatoria.clavata           0.722                  23.844   0.001
Schistomeringos.rudolphi     0.366                   0.000   0.999
Sphaerosyllis.hystrix        0.026                   9.470   0.103
Spio.filicornis              1.000                   6.560   0.319
Spisula.subtruncata          0.921                   2.197   0.953
Stenosoma.capito             0.989                   7.067   0.269
Syllis.gracilis              0.175                  21.341   0.001
Syllis.hyalina               1.000                   2.507   0.929
Tellina.tenuis               0.931                   0.000   1.000
Thracia.phaseolina           0.995                   0.000   0.999
Tricolia.pullus              0.934                  11.106   0.048
Tritia.neritea               0.998                   2.051   0.963
Tritia.reticulata            0.954                   2.073   0.961
Turbellaria                  1.000                   2.003   0.967
Upogebia.pusilla             1.000                   5.769   0.409

Arguments: with 999 resampling iterations using pit.trap resampling and response assumed to be uncorrelated 

Likelihood Ratio statistic:   1223, p-value: 0.001 

Univariate test statistic: 
         Abra.alba Abra.sp. Actiniaria Alitta.succinea Ampelisca.diadema
LR value    27.461    4.159      2.773          36.585            30.570
Pr(>LR)      0.002    0.961      0.981           0.001             0.001
         Amphibalanus.improvisus Ampithoe.sp. Anadara.kagoshimensis Apherusa.bispinosa
LR value                  23.408       12.209                 2.773              2.773
Pr(>LR)                    0.008        0.282                 0.981              0.981
         Apseudopsis.ostroumovi Bittium.reticulatum Brachynotus.sexdentatus
LR value                 52.794              34.193                   2.773
Pr(>LR)                   0.001               0.001                   0.981
         Capitella.capitata Capitella.minima Chamelea.gallina Chironomidae.larvae
LR value             33.199            7.227           28.525               9.651
Pr(>LR)               0.001            0.781            0.001               0.513
         Cumella.limicola Cumella.pygmaea Cytharella.costulata Diogenes.pugilator
LR value           41.328           6.118                7.354              3.059
Pr(>LR)             0.001           0.840                0.775              0.981
         Eteone.flava Eunice.vittata Eurydice.dollfusi Exogone.naidina
LR value        4.159          3.779             6.118           8.477
Pr(>LR)         0.961          0.967             0.840           0.642
         Gastrosaccus.sanctus Genetyllis.tuberculata Glycera.sp. Glycera.tridactyla
LR value                2.773                  7.712       7.992              5.516
Pr(>LR)                 0.981                  0.739       0.704              0.903
         Glycera.unicornis Harmothoe.imbricata Harmothoe.reticulata
LR value             2.773               8.753               15.210
Pr(>LR)              0.981               0.597                0.093
         Heteromastus.filiformis Hirudinea Hydrobia.acuta Hydrobia.sp. Iphinoe.tenella
LR value                  28.142     1.726          2.932        5.959           9.824
Pr(>LR)                    0.002     0.981          0.981        0.860           0.484
         Kellia.suborbicularis Lagis.koreni Leiochone.leiopygos Lentidium.mediterraneum
LR value                 9.077       16.471              15.331                   5.545
Pr(>LR)                  0.579        0.076               0.091                   0.897
         Lepidochitona.cinerea Loripes.orbiculatus Lucinella.divaricata
LR value                 2.773              31.348                6.172
Pr(>LR)                  0.981               0.001                0.830
         Magelona.papillicornis Maldane.glebifex Melinna.palmata
LR value                  2.773            2.773          26.860
Pr(>LR)                   0.981            0.981           0.002
         Microdeutopus.gryllotalpa Micromaldane.ornithochaeta Micronephthys.stammeri
LR value                    16.350                      6.655                  4.159
Pr(>LR)                      0.076                      0.812                  0.961
         Microphthalmus.fragilis Microphthalmus.sp. Monocorophium.acherusicum
LR value                   2.931             11.855                    39.891
Pr(>LR)                    0.981              0.306                     0.001
         Mytilaster.lineatus Mytilus.galloprovincialis Nemertea Nephtys.cirrosa
LR value              47.863                     2.773   10.046           2.773
Pr(>LR)                0.001                     0.981    0.484           0.981
         Nephtys.kersivalensis Nereis.perivisceralis Nereis.pulsatoria
LR value                 2.773                 2.773             6.238
Pr(>LR)                  0.981                 0.981             0.823
         Nototropis.guttatus Oligochaeta Paradoneis.harpagonea Parthenina.interstincta
LR value               7.210      36.765                 2.773                   4.546
Pr(>LR)                0.781       0.001                 0.981                   0.951
         Parvicardium.exiguum Perinereis.cultrifera Perioculodes.longimanus Phoronida
LR value                2.973                 6.689                   4.365     5.483
Pr(>LR)                 0.981                 0.812                   0.961     0.906
         Phyllodoce.sp. Platyhelminthes Platynereis.dumerilii Polititapes.aureus
LR value          4.159           8.508                 8.910             10.998
Pr(>LR)           0.961           0.642                 0.597              0.372
         Polychaeta.larvae Polydora.ciliata Polygordius.neapolitanus
LR value             4.159           41.905                    4.159
Pr(>LR)              0.961            0.001                    0.961
         Prionospio.cirrifera Protodorvillea.kefersteini Pseudocuma.longicorne
LR value               46.273                     30.140                 3.112
Pr(>LR)                 0.001                      0.001                 0.981
         Rissoa.membranacea Rissoa.splendida Salvatoria.clavata Schistomeringos.rudolphi
LR value              2.720           17.118             32.959                   13.822
Pr(>LR)               0.981            0.053              0.001                    0.172
         Sphaerosyllis.hystrix Spio.filicornis Spisula.subtruncata Stenosoma.capito
LR value                16.760          34.879               5.885           13.850
Pr(>LR)                  0.068           0.001               0.863            0.172
         Syllis.gracilis Syllis.hyalina Tellina.tenuis Thracia.phaseolina
LR value          28.543          4.555          4.499              2.773
Pr(>LR)            0.001          0.951          0.951              0.981
         Tricolia.pullus Tritia.neritea Tritia.reticulata Turbellaria Upogebia.pusilla
LR value          14.668          5.516            11.233       2.652           10.026
Pr(>LR)            0.118          0.903             0.353       0.981            0.484
Arguments:
 Test statistics calculated assuming response assumed to be uncorrelated 
 P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).

The factor is highly significant according to the models.

Again, save the summary for safekeeping, but also run an anova.

write_rds(glms.lvm.zostera.2.summary, 
          here(save.dir, "glms_lvm_zostera_2_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.2.aov <- anova.manyglm(glms.lvm.zostera.2, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         pairwise.comp = ~lvm.clusters.zostera.2, ## check the pairwise comparison between clusters
                                         show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.24 minutes...
    Resampling run 300 finished. Time elapsed: 0.37 minutes...
    Resampling run 400 finished. Time elapsed: 0.48 minutes...
    Resampling run 500 finished. Time elapsed: 0.60 minutes...
    Resampling run 600 finished. Time elapsed: 0.72 minutes...
    Resampling run 700 finished. Time elapsed: 0.84 minutes...
    Resampling run 800 finished. Time elapsed: 0.96 minutes...
    Resampling run 900 finished. Time elapsed: 1.08 minutes...
Time elapsed: 0 hr 1 min 12 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff  Dev Pr(>Dev)    
(Intercept)                31                          
lvm.clusters.zostera.2     27       4 1223    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Pairwise comparison results: 
                                                     Observed statistic
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:4              418.6
lvm.clusters.zostera.2:3 vs lvm.clusters.zostera.2:4              368.1
lvm.clusters.zostera.2:3 vs lvm.clusters.zostera.2:5              336.6
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:3              325.3
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:5              310.4
lvm.clusters.zostera.2:4 vs lvm.clusters.zostera.2:5              295.1
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:4              278.8
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:3              278.8
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:5              271.7
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:2              219.8
                                                     Free Stepdown Adjusted P-Value   
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:4                          0.002 **
lvm.clusters.zostera.2:3 vs lvm.clusters.zostera.2:4                          0.008 **
lvm.clusters.zostera.2:3 vs lvm.clusters.zostera.2:5                          0.009 **
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:3                          0.009 **
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:5                          0.009 **
lvm.clusters.zostera.2:4 vs lvm.clusters.zostera.2:5                          0.009 **
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:4                          0.009 **
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:3                          0.009 **
lvm.clusters.zostera.2:2 vs lvm.clusters.zostera.2:5                          0.009 **
lvm.clusters.zostera.2:1 vs lvm.clusters.zostera.2:2                          0.009 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.2    27.461    0.002    4.159    1.000      2.773    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2          36.585    0.001             30.57    0.001
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2                  23.408    0.009       12.209    0.448
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2                 2.773    1.000              2.773    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                 52.794    0.001              34.193    0.001
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                   2.773    1.000             33.199    0.001
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2            7.227    0.941           28.525    0.001
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2               9.651    0.761           41.328    0.001
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2           6.118    0.976                7.354    0.936
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.2              3.059    1.000        4.159    1.000          3.779
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2    1.000             6.118    0.976           8.477    0.879
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2                2.773    1.000                  7.712    0.926
                       Glycera.sp.          Glycera.tridactyla         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.2       7.992    0.918              5.516    0.994
                       Glycera.unicornis          Harmothoe.imbricata         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2             2.773    1.000               8.753    0.861
                       Harmothoe.reticulata          Heteromastus.filiformis         
                                        Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.2                15.21    0.180                  28.142    0.001
                       Hirudinea          Hydrobia.acuta          Hydrobia.sp.         
                             Dev Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                            
lvm.clusters.zostera.2     1.726    1.000          2.932    1.000        5.959    0.980
                       Iphinoe.tenella          Kellia.suborbicularis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2           9.824    0.747                 9.077    0.846
                       Lagis.koreni          Leiochone.leiopygos         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.2       16.471    0.131              15.331    0.179
                       Lentidium.mediterraneum          Lepidochitona.cinerea         
                                           Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                   5.545    0.990                 2.773    1.000
                       Loripes.orbiculatus          Lucinella.divaricata         
                                       Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2              31.348    0.001                6.172    0.974
                       Magelona.papillicornis          Maldane.glebifex         
                                          Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.2                  2.773    1.000            2.773    1.000
                       Melinna.palmata          Microdeutopus.gryllotalpa         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.2           26.86    0.002                     16.35    0.131
                       Micromaldane.ornithochaeta          Micronephthys.stammeri
                                              Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
lvm.clusters.zostera.2                      6.655    0.962                  4.159
                                Microphthalmus.fragilis          Microphthalmus.sp.
                       Pr(>Dev)                     Dev Pr(>Dev)                Dev
(Intercept)                                                                        
lvm.clusters.zostera.2    0.999                   2.931    1.000             11.855
                                Monocorophium.acherusicum          Mytilaster.lineatus
                       Pr(>Dev)                       Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
lvm.clusters.zostera.2    0.487                    39.891    0.001              47.863
                                Mytilus.galloprovincialis          Nemertea         
                       Pr(>Dev)                       Dev Pr(>Dev)      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2    0.001                     2.773    1.000   10.046    0.723
                       Nephtys.cirrosa          Nephtys.kersivalensis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2           2.773    1.000                 2.773    1.000
                       Nereis.perivisceralis          Nereis.pulsatoria         
                                         Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.2                 2.773    1.000             6.238    0.971
                       Nototropis.guttatus          Oligochaeta         
                                       Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                             
lvm.clusters.zostera.2                7.21    0.941      36.765    0.001
                       Paradoneis.harpagonea          Parthenina.interstincta         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                 2.773    1.000                   4.546    0.997
                       Parvicardium.exiguum          Perinereis.cultrifera         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                2.973    1.000                 6.689    0.962
                       Perioculodes.longimanus          Phoronida         
                                           Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2                   4.365    0.999     5.483    0.994
                       Phyllodoce.sp.          Platyhelminthes         
                                  Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.2          4.159    1.000           8.508    0.879
                       Platynereis.dumerilii          Polititapes.aureus         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2                  8.91    0.851             10.998    0.575
                       Polychaeta.larvae          Polydora.ciliata         
                                     Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                
lvm.clusters.zostera.2             4.159    0.999           41.905    0.001
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                    4.159    0.999               46.273    0.001
                       Protodorvillea.kefersteini          Pseudocuma.longicorne
                                              Dev Pr(>Dev)                   Dev
(Intercept)                                  <NA>     <NA>                  <NA>
lvm.clusters.zostera.2                      30.14    0.001                 3.112
                                Rissoa.membranacea          Rissoa.splendida         
                       Pr(>Dev)                Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                <NA>               <NA>     <NA>             <NA>     <NA>
lvm.clusters.zostera.2    1.000               2.72    1.000           17.118    0.113
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                          <NA>     <NA>                     <NA>     <NA>
lvm.clusters.zostera.2             32.959    0.001                   13.822    0.291
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                             <NA>     <NA>            <NA>     <NA>
lvm.clusters.zostera.2                 16.76    0.124          34.879    0.001
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                           <NA>     <NA>             <NA>     <NA>
lvm.clusters.zostera.2               5.885    0.980            13.85    0.291
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                       <NA>     <NA>           <NA>     <NA>           <NA>
lvm.clusters.zostera.2          28.543    0.001          4.555    0.997          4.499
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                <NA>               <NA>     <NA>            <NA>     <NA>
lvm.clusters.zostera.2    0.997              2.773    1.000          14.668    0.223
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                      <NA>     <NA>              <NA>     <NA>        <NA>
lvm.clusters.zostera.2          5.516    0.994            11.233    0.558       2.652
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                <NA>             <NA>     <NA>
lvm.clusters.zostera.2    1.000           10.026    0.723
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Again, these groups are sufficiently different from one another.. No clue here.

Save the ANOVA, too.

write_rds(glms.lvm.zostera.2.aov, 
          here(save.dir, "glms_lvm_zostera_2_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.2 <- top_n_sp_glm(glms.lvm.zostera.2.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.799"
    Apseudopsis.ostroumovi        Mytilaster.lineatus       Prionospio.cirrifera 
                 52.793744                  47.863335                  46.272692 
          Polydora.ciliata           Cumella.limicola  Monocorophium.acherusicum 
                 41.905219                  41.327723                  39.891356 
               Oligochaeta            Alitta.succinea            Spio.filicornis 
                 36.764590                  36.584687                  34.878811 
       Bittium.reticulatum         Capitella.capitata         Salvatoria.clavata 
                 34.192799                  33.198554                  32.958829 
       Loripes.orbiculatus          Ampelisca.diadema Protodorvillea.kefersteini 
                 31.347733                  30.569510                  30.139960 
           Syllis.gracilis           Chamelea.gallina    Heteromastus.filiformis 
                 28.542915                  28.524575                  28.142266 
                 Abra.alba            Melinna.palmata    Amphibalanus.improvisus 
                 27.461185                  26.859546                  23.408099 
          Rissoa.splendida      Sphaerosyllis.hystrix               Lagis.koreni 
                 17.117581                  16.760313                  16.471224 
 Microdeutopus.gryllotalpa        Leiochone.leiopygos       Harmothoe.reticulata 
                 16.349670                  15.331303                  15.209809 
           Tricolia.pullus           Stenosoma.capito   Schistomeringos.rudolphi 
                 14.667741                  13.849706                  13.822279 
              Ampithoe.sp.         Microphthalmus.sp.          Tritia.reticulata 
                 12.208710                  11.854688                  11.232600 
        Polititapes.aureus                   Nemertea           Upogebia.pusilla 
                 10.998455                  10.045834                  10.025894 
           Iphinoe.tenella        Chironomidae.larvae      Kellia.suborbicularis 
                  9.824385                   9.650905                   9.077281 
     Platynereis.dumerilii 
                  8.910425 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.2) <- names(top.sp.glms.lvm.zostera.2) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.2
    Apseudopsis ostroumovi        Mytilaster lineatus       Prionospio cirrifera 
                 52.793744                  47.863335                  46.272692 
          Polydora ciliata           Cumella limicola  Monocorophium acherusicum 
                 41.905219                  41.327723                  39.891356 
               Oligochaeta            Alitta succinea            Spio filicornis 
                 36.764590                  36.584687                  34.878811 
       Bittium reticulatum         Capitella capitata         Salvatoria clavata 
                 34.192799                  33.198554                  32.958829 
       Loripes orbiculatus          Ampelisca diadema Protodorvillea kefersteini 
                 31.347733                  30.569510                  30.139960 
           Syllis gracilis           Chamelea gallina    Heteromastus filiformis 
                 28.542915                  28.524575                  28.142266 
                 Abra alba            Melinna palmata    Amphibalanus improvisus 
                 27.461185                  26.859546                  23.408099 
          Rissoa splendida      Sphaerosyllis hystrix               Lagis koreni 
                 17.117581                  16.760313                  16.471224 
 Microdeutopus gryllotalpa        Leiochone leiopygos       Harmothoe reticulata 
                 16.349670                  15.331303                  15.209809 
           Tricolia pullus           Stenosoma capito   Schistomeringos rudolphi 
                 14.667741                  13.849706                  13.822279 
              Ampithoe sp.         Microphthalmus sp.          Tritia reticulata 
                 12.208710                  11.854688                  11.232600 
        Polititapes aureus                   Nemertea           Upogebia pusilla 
                 10.998455                  10.045834                  10.025894 
           Iphinoe tenella        Chironomidae larvae      Kellia suborbicularis 
                  9.824385                   9.650905                   9.077281 
     Platynereis dumerilii 
                  8.910425 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.2 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.2)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.2)))) %>% 
   mutate(group = factor(case_when(station == "Poda" ~ 1,
                                   station == "Otmanli" ~ 2,
                                   station == "Vromos" ~ 3, 
                                   station == "Gradina" ~ 4, 
                                   station == "Ropotamo" ~ 5)))
)
(plot.top.sp.glms.lvm.zostera.2 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.2,
                                              mapping = aes(x = species, y = log_y_min(count), colour = group),
                                              labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.2$group))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())
)

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.2
[[1]]

[[2]]

[[3]]

[[4]]

[[5]]
NA

In the case of the seagrasses and case 2 clusters (= stations), the picture is still more unclear.. I suppose this is in no small part because of the differences 2013-14 - very marked for Poda and Otmanli. I suspect the stations changed in these two years (we were looking for Z. noltii in 2014 in particular) - but still, there is much variability. In the future, it’s probably going to be worth it to have more stations in a meadow, if we really want to have an idea of the communities there, and their variability.
The LRs seem to be a bit lower for groups 2, 4, maybe 5 too - still not sure if you can use that as a significance measure.
For now, in group 1 (= Z1), it’s hard to pick some characteristic species - because of the variability between 2013-2014, no doubt. The species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Polydora ciliata, Prionosprio cirrifera (+ others, medium abundance); and the ones with a significantly lower abundance - or even absent - C. gallina, A. ostroumovi, S. clavata, C. limicola, C. costulata, S. hystrix, S. gracilis, T. pullus.
For group 2 (= Z2), the species with higher abundance - which is not really all that high; this group is also loose, hard to distinguish from group 1 - are: S. gracilis, M. lineatus, P. ciliata. The only species with lower abundance - in fact 0 - is Alitta succinea.
For group 3 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A. diadema. The species with lower abundance (or 0) are: B. reticulatum, P. ciliata, P. cirrifera, A. alba, A. succinea, S. clavata, Oligochaeta, A. improvisus.
For group 4 (= Z4), the species with higher abundance are: M. lineatus (very much so); C. limicola, P. kefersteini, C. gallina, C. capitata. The species with lower abundance (or 0) are: P. ciliata, P. cirrifera, A. succinea, A. improvisus, A. alba.
For group 5 (= Z5), the species with higher abundance are: A. ostroumovi, C. capitata, Oligochaeta. The species with lower abundance (or 0) are: R. splendida, T. pullus.

LVM clusters - case 3 Last try: group 1 = Z1-Z2, group 2 = Z3, group 3 = Z4, group 4 = Z5.
Check the model assumptions.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, table = TRUE)
START SECTION 2 
Plotting if overlay is TRUE
using grouping variable lvm.clusters.zostera.3 160 mean values were 0 and could 
                                        not be included in the log-plot
using grouping variable lvm.clusters.zostera.3 160 variance values were 0 and could not 
                                        be included in the log-plot
FINISHED SECTION 2 
$mean
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1             57.6875          50.8125     30.0625              6.25               3.250
2              0.0000          88.0000      0.7500             80.50               2.250
3            238.3750          23.1250     48.6250             24.50              76.375
4             74.2500         124.0000    201.2500             20.25               2.750
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1                 17.8125               25.375          26.5625
2                  2.2500                0.000           0.0000
3                 23.0000                0.000           0.2500
4                  5.2500               20.000          11.2500
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                    3.9375             7.4375             0.4375                 0.0625
2                   78.2500             9.5000             0.0000                 0.0000
3                    1.0000            10.1250             9.8750                 3.8750
4                    2.2500             4.0000            39.7500                48.2500
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1          1.4375                     2.625    6.3125            0.375
2         38.2500                     4.250    0.0000            0.000
3          1.2500                     1.875    0.7500           10.250
4          0.0000                    14.000    1.7500            6.500
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1               1.125               2.8125                      0.750
2               0.500               5.5000                      0.000
3               8.750               2.8750                      9.875
4               4.500               1.5000                      1.250
  Platynereis.dumerilii Nemertea Syllis.gracilis Alitta.succinea Amphibalanus.improvisus
1                1.5625    2.375           1.625          3.5625                  3.3125
2                9.2500    0.500           0.000          0.0000                  0.2500
3                1.6250    3.125           0.875          0.0000                  0.2500
4                3.7500    1.500           7.250          1.0000                  0.5000
  Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi Salvatoria.clavata
1            1.500        2.125                   1.6875              0.000
2            0.000        0.000                   0.0000              1.500
3            0.875        1.125                   1.2500              0.375
4            3.750        0.500                   0.0000              6.250
  Leiochone.leiopygos Melinna.palmata Microphthalmus.sp. Kellia.suborbicularis
1               0.625           0.875              0.000                0.3125
2               0.000           2.750              0.000                0.0000
3               1.875           0.000              0.625                2.3750
4               0.000           0.000              5.000                0.0000
  Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera Sphaerosyllis.hystrix
1               0.750           0.0625                0.4375                0.1875
2               0.000           0.0000                0.0000                0.0000
3               0.125           2.0000                0.6250                1.3750
4               2.500           1.2500                2.0000                1.2500
  Ampithoe.sp. Harmothoe.reticulata Phoronida Perioculodes.longimanus Rissoa.splendida
1       0.1875                0.750    0.5625                   0.375             0.00
2       2.7500                0.000    0.0000                   1.250             1.00
3       0.5000                0.125    0.7500                   0.125             0.25
4       0.0000                1.000    0.2500                   0.750             2.25
  Diogenes.pugilator Iphinoe.tenella Platyhelminthes Exogone.naidina
1              0.375          0.6875          0.6875          0.0625
2              0.750          0.0000          0.0000          2.2500
3              0.250          0.2500          0.2500          0.2500
4              0.750          0.0000          0.0000          0.0000
  Genetyllis.tuberculata Parthenina.interstincta Tritia.reticulata Cytharella.costulata
1                  0.500                   0.625            0.5625               0.1875
2                  0.250                   0.000            0.0000               0.2500
3                  0.375                   0.250            0.2500               0.6250
4                  0.000                   0.000            0.2500               0.5000
  Syllis.hyalina Tricolia.pullus Turbellaria Harmothoe.imbricata Hydrobia.sp.
1            0.0          0.0625       0.375              0.3125        0.375
2            0.0          0.0000       0.250              0.0000        0.000
3            0.0          0.2500       0.375              0.2500        0.125
4            2.5          1.7500       0.000              0.0000        0.000
  Lucinella.divaricata Nereis.pulsatoria Polititapes.aureus Upogebia.pusilla Glycera.sp.
1                0.000            0.4375              0.375             0.00       0.375
2                0.000            0.0000              0.000             0.00       0.000
3                0.875            0.0000              0.125             0.00       0.000
4                0.000            0.0000              0.000             1.75       0.000
  Microphthalmus.fragilis Eunice.vittata Glycera.tridactyla Tritia.neritea
1                   0.375         0.1875             0.3125          0.250
2                   0.000         0.0000             0.0000          0.000
3                   0.000         0.0000             0.0000          0.125
4                   0.000         0.5000             0.0000          0.000
  Chironomidae.larvae Hydrobia.acuta Micromaldane.ornithochaeta Cumella.pygmaea
1                   0           0.25                      0.000           0.000
2                   0           0.00                      0.250           0.000
3                   0           0.00                      0.375           0.375
4                   1           0.00                      0.000           0.000
  Eurydice.dollfusi Hirudinea Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis
1             0.000     0.125                0.0625                0.00         0.0625
2             0.000     0.000                0.0000                0.00         0.0000
3             0.375     0.125                0.1250                0.25         0.2500
4             0.000     0.000                0.2500                0.25         0.0000
  Brachynotus.sexdentatus Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa
1                  0.0625                    0.00                 0.0625          0.0625
2                  0.0000                    0.00                 0.0000          0.0000
3                  0.1250                    0.25                 0.0000          0.1250
4                  0.0000                    0.00                 0.2500          0.0000
  Abra.sp. Actiniaria Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava
1     0.00     0.0625                0.0625              0.000         0.00
2     0.25     0.0000                0.0000              0.000         0.25
3     0.00     0.0000                0.0000              0.125         0.00
4     0.00     0.0000                0.0000              0.000         0.00
  Gastrosaccus.sanctus Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis
1                0.000            0.0625                 0.000                  0.000
2                0.000            0.0000                 0.000                  0.000
3                0.125            0.0000                 0.125                  0.125
4                0.000            0.0000                 0.000                  0.000
  Maldane.glebifex Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1           0.0625                    0.0625                0.0625                 0.000
2           0.0000                    0.0000                0.0000                 0.000
3           0.0000                    0.0000                0.0000                 0.125
4           0.0000                    0.0000                0.0000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
4                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.125
4              0.000

$var
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1            2642.229        2899.2292    700.8625          45.53333           35.000000
2               0.000        3094.0000      2.2500         395.00000            1.583333
3           25180.554         452.6964   3778.2679         735.14286          877.125000
4            3278.250        3103.3333  18570.9167          92.91667            2.916667
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1              177.495833             919.5833     1000.2625000
2                1.583333               0.0000        0.0000000
3              136.000000               0.0000        0.2142857
4               32.916667             183.3333       34.2500000
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                 17.929167         271.729167           1.595833               0.062500
2               3980.916667          11.666667           0.000000               0.000000
3                  1.428571          95.553571          82.982143               9.839286
4                  4.250000           6.666667         566.250000             196.250000
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1        2.529167                 10.783333 24.362500         1.183333
2      306.250000                 16.250000  0.000000         0.000000
3        3.357143                  2.696429  1.071429        30.500000
4        0.000000                 40.666667  1.583333        23.000000
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1            2.383333            18.829167                    2.60000
2            1.000000             3.666667                    0.00000
3           16.500000             8.410714                   16.69643
4            7.000000             1.666667                    2.25000
  Platynereis.dumerilii   Nemertea Syllis.gracilis Alitta.succinea
1              6.929167 12.2500000        7.450000      30.1291667
2             32.916667  0.3333333        0.000000       0.0000000
3              2.553571  3.8392857        2.982143       0.0000000
4             10.916667  3.6666667       22.916667       0.6666667
  Amphibalanus.improvisus Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi
1              23.4291667       19.7333333    6.5166667                11.295833
2               0.2500000        0.0000000    0.0000000                 0.000000
3               0.2142857        0.9821429    0.9821429                 3.642857
4               1.0000000       12.9166667    0.3333333                 0.000000
  Salvatoria.clavata Leiochone.leiopygos Melinna.palmata Microphthalmus.sp.
1          0.0000000            0.650000        1.183333              0.000
2          0.3333333            0.000000        0.250000              0.000
3          1.1250000            3.839286        0.000000              3.125
4         14.9166667            0.000000        0.000000             22.000
  Kellia.suborbicularis Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera
1             0.6291667            1.666667         0.062500             2.2625000
2             0.0000000            0.000000         0.000000             0.0000000
3            13.6964286            0.125000         1.714286             0.8392857
4             0.0000000           14.333333         1.583333             3.3333333
  Sphaerosyllis.hystrix Ampithoe.sp. Harmothoe.reticulata Phoronida
1             0.2958333    0.2958333            0.7333333 0.5291667
2             0.0000000   11.5833333            0.0000000 0.0000000
3             2.2678571    0.5714286            0.1250000 1.0714286
4             0.9166667    0.0000000            2.0000000 0.2500000
  Perioculodes.longimanus Rissoa.splendida Diogenes.pugilator Iphinoe.tenella
1               0.5166667        0.0000000          0.3833333        2.229167
2               3.5833333        2.0000000          0.2500000        0.000000
3               0.1250000        0.2142857          0.2142857        0.500000
4               0.9166667        6.9166667          0.9166667        0.000000
  Platyhelminthes Exogone.naidina Genetyllis.tuberculata Parthenina.interstincta
1       1.4291667          0.0625              2.2666667                    2.65
2       0.0000000          8.2500              0.2500000                    0.00
3       0.2142857          0.5000              0.5535714                    0.50
4       0.0000000          0.0000              0.0000000                    0.00
  Tritia.reticulata Cytharella.costulata Syllis.hyalina Tricolia.pullus Turbellaria
1         1.4625000            0.1625000              0       0.0625000       1.050
2         0.0000000            0.2500000              0       0.0000000       0.250
3         0.2142857            0.8392857              0       0.2142857       1.125
4         0.2500000            0.3333333             25       2.9166667       0.000
  Harmothoe.imbricata Hydrobia.sp. Lucinella.divaricata Nereis.pulsatoria
1           0.6291667     1.183333             0.000000            1.4625
2           0.0000000     0.000000             0.000000            0.0000
3           0.2142857     0.125000             3.267857            0.0000
4           0.0000000     0.000000             0.000000            0.0000
  Polititapes.aureus Upogebia.pusilla Glycera.sp. Microphthalmus.fragilis Eunice.vittata
1              0.650         0.000000   0.3833333                    2.25      0.2958333
2              0.000         0.000000   0.0000000                    0.00      0.0000000
3              0.125         0.000000   0.0000000                    0.00      0.0000000
4              0.000         5.583333   0.0000000                    0.00      1.0000000
  Glycera.tridactyla Tritia.neritea Chironomidae.larvae Hydrobia.acuta
1          0.6291667          0.600                   0              1
2          0.0000000          0.000                   0              0
3          0.0000000          0.125                   0              0
4          0.0000000          0.000                   2              0
  Micromaldane.ornithochaeta Cumella.pygmaea Eurydice.dollfusi Hirudinea
1                  0.0000000       0.0000000         0.0000000 0.1166667
2                  0.2500000       0.0000000         0.0000000 0.0000000
3                  0.5535714       0.5535714         0.5535714 0.1250000
4                  0.0000000       0.0000000         0.0000000 0.0000000
  Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis Brachynotus.sexdentatus
1                0.0625           0.0000000      0.0625000                  0.0625
2                0.0000           0.0000000      0.0000000                  0.0000
3                0.1250           0.2142857      0.2142857                  0.1250
4                0.2500           0.2500000      0.0000000                  0.0000
  Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa Abra.sp. Actiniaria
1               0.0000000                 0.0625          0.0625     0.00     0.0625
2               0.0000000                 0.0000          0.0000     0.25     0.0000
3               0.2142857                 0.0000          0.1250     0.00     0.0000
4               0.0000000                 0.2500          0.0000     0.00     0.0000
  Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava Gastrosaccus.sanctus
1                0.0625              0.000         0.00                0.000
2                0.0000              0.000         0.25                0.000
3                0.0000              0.125         0.00                0.125
4                0.0000              0.000         0.00                0.000
  Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis Maldane.glebifex
1            0.0625                 0.000                  0.000           0.0625
2            0.0000                 0.000                  0.000           0.0000
3            0.0000                 0.125                  0.125           0.0000
4            0.0000                 0.000                  0.000           0.0000
  Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1                    0.0625                0.0625                 0.000
2                    0.0000                0.0000                 0.000
3                    0.0000                0.0000                 0.125
4                    0.0000                0.0000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
4                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.125
4              0.000

More or less the same as case 2 before it.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.3 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.3)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.3, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(3,3))
# lapply(3:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(3, 3))

Save the model!

write_rds(glms.lvm.zostera.3, 
          here(save.dir, "glms_lvm_zostera_3.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

glms.lvm.zostera.3.summary

Test statistics:
                        LR value Pr(>LR)    
(Intercept)               1394.5   0.001 ***
lvm.clusters.zostera.32    358.1   0.001 ***
lvm.clusters.zostera.33    423.5   0.001 ***
lvm.clusters.zostera.34    335.3   0.001 ***
--- 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Univariate test statistic: 
                           (Intercept)         lvm.clusters.zostera.32        
                              LR value Pr(>LR)                LR value Pr(>LR)
Abra.alba                       47.727   0.001                  18.148   0.004
Abra.sp.                         6.107   0.547                   3.219   0.632
Actiniaria                       2.833   0.939                   0.446   0.990
Alitta.succinea                  8.284   0.276                   5.558   0.259
Ampelisca.diadema               45.273   0.001                  20.069   0.002
Amphibalanus.improvisus         15.404   0.025                   5.997   0.240
Ampithoe.sp.                     5.782   0.605                   6.490   0.224
Anadara.kagoshimensis            2.833   0.939                   0.446   0.990
Apherusa.bispinosa               5.024   0.728                   0.000   1.000
Apseudopsis.ostroumovi          21.836   0.019                   0.445   0.990
Bittium.reticulatum            159.822   0.001                  25.436   0.002
Brachynotus.sexdentatus          4.881   0.753                   0.446   0.990
Capitella.capitata               3.390   0.925                   2.606   0.762
Capitella.minima               158.885   0.001                   0.860   0.984
Chamelea.gallina                21.471   0.019                   0.446   0.990
Chironomidae.larvae              9.401   0.220                   0.000   0.996
Cumella.limicola                 6.366   0.532                   2.538   0.774
Cumella.pygmaea                  7.559   0.402                   0.000   1.000
Cytharella.costulata            10.276   0.177                   0.059   0.996
Diogenes.pugilator               7.671   0.396                   0.877   0.984
Eteone.flava                     6.107   0.547                   3.219   0.632
Eunice.vittata                   3.020   0.926                   1.027   0.968
Eurydice.dollfusi                7.559   0.402                   0.000   1.000
Exogone.naidina                  6.206   0.534                   5.880   0.240
Gastrosaccus.sanctus             5.024   0.728                   0.000   1.000
Genetyllis.tuberculata           0.996   0.986                   0.185   0.996
Glycera.sp.                      4.780   0.753                   2.664   0.745
Glycera.tridactyla               2.091   0.973                   1.471   0.930
Glycera.unicornis                2.833   0.939                   0.446   0.990
Harmothoe.imbricata              3.139   0.926                   1.743   0.883
Harmothoe.reticulata             0.997   0.986                   5.096   0.313
Heteromastus.filiformis        123.751   0.001                  11.936   0.030
Hirudinea                        5.835   0.594                   0.893   0.984
Hydrobia.acuta                   0.471   0.986                   0.467   0.989
Hydrobia.sp.                     0.941   0.986                   1.166   0.950
Iphinoe.tenella                  0.542   0.986                   2.867   0.704
Kellia.suborbicularis            2.897   0.939                   1.598   0.914
Lagis.koreni                     6.615   0.510                   8.571   0.108
Leiochone.leiopygos              1.958   0.977                   4.059   0.486
Lentidium.mediterraneum          9.353   0.224                   0.000   0.996
Lepidochitona.cinerea            5.024   0.728                   0.000   1.000
Loripes.orbiculatus              0.205   0.986                   1.283   0.950
Lucinella.divaricata             5.816   0.600                   0.000   1.000
Magelona.papillicornis           5.024   0.728                   0.000   1.000
Maldane.glebifex                 2.833   0.939                   0.446   0.990
Melinna.palmata                  0.261   0.986                   6.839   0.200
Microdeutopus.gryllotalpa       13.341   0.044                   0.870   0.984
Micromaldane.ornithochaeta       9.788   0.198                   3.053   0.656
Micronephthys.stammeri           5.710   0.605                   0.446   0.990
Microphthalmus.fragilis          0.234   0.986                   0.467   0.989
Microphthalmus.sp.               9.420   0.219                   0.000   1.000
Monocorophium.acherusicum       26.934   0.005                  26.810   0.001
Mytilaster.lineatus             17.441   0.019                   0.324   0.993
Mytilus.galloprovincialis        2.833   0.939                   0.446   0.990
Nemertea                         9.059   0.233                   3.320   0.631
Nephtys.cirrosa                  4.881   0.753                   0.446   0.990
Nephtys.kersivalensis            2.833   0.939                   0.446   0.990
Nereis.perivisceralis            5.024   0.728                   0.000   1.000
Nereis.pulsatoria                0.491   0.986                   0.980   0.971
Nototropis.guttatus              0.323   0.986                   2.976   0.669
Oligochaeta                    126.966   0.001                  15.119   0.007
Paradoneis.harpagonea            2.833   0.939                   0.446   0.990
Parthenina.interstincta          0.301   0.986                   1.536   0.924
Parvicardium.exiguum            14.018   0.039                   1.502   0.930
Perinereis.cultrifera            1.844   0.981                   2.060   0.867
Perioculodes.longimanus          3.981   0.870                   2.049   0.869
Phoronida                        3.161   0.926                   3.937   0.509
Phyllodoce.sp.                   6.107   0.547                   3.219   0.632
Platyhelminthes                  0.644   0.986                   3.118   0.642
Platynereis.dumerilii            1.824   0.981                   7.414   0.173
Polititapes.aureus               2.789   0.939                   2.081   0.863
Polychaeta.larvae                6.107   0.547                   3.219   0.632
Polydora.ciliata                81.609   0.001                  15.796   0.005
Polygordius.neapolitanus         6.107   0.547                   3.219   0.632
Prionospio.cirrifera            91.317   0.001                  19.403   0.002
Protodorvillea.kefersteini       0.820   0.986                   4.746   0.362
Pseudocuma.longicorne            7.101   0.453                   0.446   0.990
Rissoa.membranacea              50.503   0.001                   0.160   0.996
Rissoa.splendida                17.291   0.019                  10.624   0.047
Salvatoria.clavata              25.703   0.006                  18.216   0.004
Schistomeringos.rudolphi         0.703   0.986                   2.760   0.729
Sphaerosyllis.hystrix           10.217   0.179                   1.307   0.949
Spio.filicornis                  1.763   0.981                  24.367   0.002
Spisula.subtruncata             11.731   0.089                   0.000   1.000
Stenosoma.capito                 1.007   0.986                   4.916   0.344
Syllis.gracilis                  1.598   0.981                   5.347   0.283
Syllis.hyalina                   3.627   0.894                   0.000   0.996
Tellina.tenuis                   7.795   0.377                   0.446   0.990
Thracia.phaseolina               5.024   0.728                   0.000   1.000
Tricolia.pullus                 13.409   0.043                   0.445   0.990
Tritia.neritea                   1.950   0.978                   1.104   0.961
Tritia.reticulata                1.128   0.983                   2.531   0.777
Turbellaria                      1.449   0.981                   0.056   0.996
Upogebia.pusilla                 8.660   0.248                   0.000   1.000
                           lvm.clusters.zostera.33         lvm.clusters.zostera.34
                                          LR value Pr(>LR)                LR value
Abra.alba                                   15.271   0.010                   4.994
Abra.sp.                                     0.000   1.000                   0.000
Actiniaria                                   0.811   1.000                   0.446
Alitta.succinea                              9.839   0.093                   1.072
Ampelisca.diadema                            8.950   0.133                   4.744
Amphibalanus.improvisus                     10.321   0.082                   4.259
Ampithoe.sp.                                 1.064   1.000                   1.175
Anadara.kagoshimensis                        0.811   1.000                   0.446
Apherusa.bispinosa                           2.197   0.995                   0.000
Apseudopsis.ostroumovi                      32.536   0.001                  46.727
Bittium.reticulatum                         10.139   0.084                   0.217
Brachynotus.sexdentatus                      0.236   1.000                   0.446
Capitella.capitata                          18.553   0.002                  25.101
Capitella.minima                             2.320   0.991                   2.355
Chamelea.gallina                            22.820   0.002                  11.133
Chironomidae.larvae                          0.000   1.000                   7.676
Cumella.limicola                            27.637   0.001                  20.452
Cumella.pygmaea                              4.909   0.612                   0.000
Cytharella.costulata                         2.833   0.963                   1.046
Diogenes.pugilator                           0.263   1.000                   0.877
Eteone.flava                                 0.000   1.000                   0.000
Eunice.vittata                               1.873   0.999                   0.483
Eurydice.dollfusi                            4.909   0.612                   0.000
Exogone.naidina                              1.012   1.000                   0.416
Gastrosaccus.sanctus                         2.197   0.995                   0.000
Genetyllis.tuberculata                       0.063   1.000                   1.888
Glycera.sp.                                  4.773   0.632                   2.664
Glycera.tridactyla                           2.652   0.977                   1.471
Glycera.unicornis                            0.811   1.000                   0.446
Harmothoe.imbricata                          0.047   1.000                   1.743
Harmothoe.reticulata                         4.553   0.677                   0.222
Heteromastus.filiformis                      0.653   1.000                   5.770
Hirudinea                                    0.000   1.000                   0.893
Hydrobia.acuta                               0.845   1.000                   0.467
Hydrobia.sp.                                 0.396   1.000                   1.166
Iphinoe.tenella                              0.979   1.000                   2.867
Kellia.suborbicularis                        4.332   0.730                   1.598
Lagis.koreni                                 1.378   1.000                   2.889
Leiochone.leiopygos                          4.772   0.633                   4.059
Lentidium.mediterraneum                      4.394   0.718                   0.000
Lepidochitona.cinerea                        2.197   0.995                   0.000
Loripes.orbiculatus                         23.881   0.002                   9.848
Lucinella.divaricata                         4.958   0.603                   0.000
Magelona.papillicornis                       2.197   0.995                   0.000
Maldane.glebifex                             0.811   1.000                   0.446
Melinna.palmata                             11.353   0.053                   6.248
Microdeutopus.gryllotalpa                    0.549   1.000                  10.829
Micromaldane.ornithochaeta                   5.601   0.498                   0.000
Micronephthys.stammeri                       0.811   1.000                   0.893
Microphthalmus.fragilis                      0.845   1.000                   0.467
Microphthalmus.sp.                           6.434   0.390                  10.604
Monocorophium.acherusicum                    6.554   0.382                   0.880
Mytilaster.lineatus                         28.164   0.001                   0.072
Mytilus.galloprovincialis                    0.811   1.000                   0.446
Nemertea                                     0.344   1.000                   0.460
Nephtys.cirrosa                              0.236   1.000                   0.446
Nephtys.kersivalensis                        0.811   1.000                   0.446
Nereis.perivisceralis                        2.197   0.995                   0.000
Nereis.pulsatoria                            1.766   0.999                   0.980
Nototropis.guttatus                          2.256   0.995                   1.529
Oligochaeta                                  1.311   1.000                  12.946
Paradoneis.harpagonea                        0.811   1.000                   0.446
Parthenina.interstincta                      0.348   1.000                   1.536
Parvicardium.exiguum                         0.002   1.000                   0.885
Perinereis.cultrifera                        0.146   1.000                   2.073
Perioculodes.longimanus                      1.060   1.000                   0.584
Phoronida                                    0.286   1.000                   0.722
Phyllodoce.sp.                               0.000   1.000                   0.000
Platyhelminthes                              1.116   1.000                   3.118
Platynereis.dumerilii                        0.005   1.000                   1.755
Polititapes.aureus                           0.920   1.000                   2.081
Polychaeta.larvae                            0.000   1.000                   0.000
Polydora.ciliata                            20.565   0.002                   1.275
Polygordius.neapolitanus                     0.000   1.000                   0.000
Prionospio.cirrifera                        31.954   0.001                   0.160
Protodorvillea.kefersteini                  18.752   0.002                   0.636
Pseudocuma.longicorne                        0.236   1.000                   0.893
Rissoa.membranacea                           0.416   1.000                   0.818
Rissoa.splendida                             4.195   0.748                  16.268
Salvatoria.clavata                           6.518   0.382                  31.870
Schistomeringos.rudolphi                     0.066   1.000                   2.760
Sphaerosyllis.hystrix                        8.440   0.170                   5.462
Spio.filicornis                              0.088   1.000                   7.758
Spisula.subtruncata                          4.394   0.719                   3.219
Stenosoma.capito                             0.492   1.000                   1.211
Syllis.gracilis                              0.703   1.000                   3.662
Syllis.hyalina                               0.000   1.000                   3.584
Tellina.tenuis                               1.386   1.000                   0.446
Thracia.phaseolina                           2.197   0.995                   0.000
Tricolia.pullus                              1.365   1.000                  11.315
Tritia.neritea                               0.205   1.000                   1.104
Tritia.reticulata                            0.624   1.000                   0.361
Turbellaria                                  0.000   1.000                   1.475
Upogebia.pusilla                             0.000   1.000                   8.030
                                  
                           Pr(>LR)
Abra.alba                    0.596
Abra.sp.                     1.000
Actiniaria                   1.000
Alitta.succinea              1.000
Ampelisca.diadema            0.632
Amphibalanus.improvisus      0.702
Ampithoe.sp.                 1.000
Anadara.kagoshimensis        1.000
Apherusa.bispinosa           1.000
Apseudopsis.ostroumovi       0.001
Bittium.reticulatum          1.000
Brachynotus.sexdentatus      1.000
Capitella.capitata           0.001
Capitella.minima             0.965
Chamelea.gallina             0.068
Chironomidae.larvae          0.237
Cumella.limicola             0.001
Cumella.pygmaea              1.000
Cytharella.costulata         1.000
Diogenes.pugilator           1.000
Eteone.flava                 1.000
Eunice.vittata               1.000
Eurydice.dollfusi            1.000
Exogone.naidina              1.000
Gastrosaccus.sanctus         1.000
Genetyllis.tuberculata       0.988
Glycera.sp.                  0.944
Glycera.tridactyla           0.997
Glycera.unicornis            1.000
Harmothoe.imbricata          0.991
Harmothoe.reticulata         1.000
Heteromastus.filiformis      0.459
Hirudinea                    1.000
Hydrobia.acuta               1.000
Hydrobia.sp.                 1.000
Iphinoe.tenella              0.903
Kellia.suborbicularis        0.995
Lagis.koreni                 0.903
Leiochone.leiopygos          0.735
Lentidium.mediterraneum      1.000
Lepidochitona.cinerea        1.000
Loripes.orbiculatus          0.104
Lucinella.divaricata         1.000
Magelona.papillicornis       1.000
Maldane.glebifex             1.000
Melinna.palmata              0.399
Microdeutopus.gryllotalpa    0.075
Micromaldane.ornithochaeta   1.000
Micronephthys.stammeri       1.000
Microphthalmus.fragilis      1.000
Microphthalmus.sp.           0.079
Monocorophium.acherusicum    1.000
Mytilaster.lineatus          1.000
Mytilus.galloprovincialis    1.000
Nemertea                     1.000
Nephtys.cirrosa              1.000
Nephtys.kersivalensis        1.000
Nereis.perivisceralis        1.000
Nereis.pulsatoria            1.000
Nototropis.guttatus          0.996
Oligochaeta                  0.027
Paradoneis.harpagonea        1.000
Parthenina.interstincta      0.996
Parvicardium.exiguum         1.000
Perinereis.cultrifera        0.980
Perioculodes.longimanus      1.000
Phoronida                    1.000
Phyllodoce.sp.               1.000
Platyhelminthes              0.867
Platynereis.dumerilii        0.991
Polititapes.aureus           0.979
Polychaeta.larvae            1.000
Polydora.ciliata             1.000
Polygordius.neapolitanus     1.000
Prionospio.cirrifera         1.000
Protodorvillea.kefersteini   1.000
Pseudocuma.longicorne        1.000
Rissoa.membranacea           1.000
Rissoa.splendida             0.005
Salvatoria.clavata           0.001
Schistomeringos.rudolphi     0.926
Sphaerosyllis.hystrix        0.498
Spio.filicornis              0.233
Spisula.subtruncata          0.854
Stenosoma.capito             1.000
Syllis.gracilis              0.797
Syllis.hyalina               0.797
Tellina.tenuis               1.000
Thracia.phaseolina           1.000
Tricolia.pullus              0.060
Tritia.neritea               1.000
Tritia.reticulata            1.000
Turbellaria                  0.997
Upogebia.pusilla             0.216

Arguments: with 999 resampling iterations using pit.trap resampling and response assumed to be uncorrelated 

Likelihood Ratio statistic:  965.7, p-value: 0.001 

Univariate test statistic: 
         Abra.alba Abra.sp. Actiniaria Alitta.succinea Ampelisca.diadema
LR value    27.438    4.159      1.386          13.528            20.153
Pr(>LR)      0.002    0.933      0.994           0.119             0.010
         Amphibalanus.improvisus Ampithoe.sp. Anadara.kagoshimensis Apherusa.bispinosa
LR value                  15.231        8.727                 1.386              2.773
Pr(>LR)                    0.076        0.517                 0.994              0.983
         Apseudopsis.ostroumovi Bittium.reticulatum Brachynotus.sexdentatus
LR value                 51.414              34.189                   1.386
Pr(>LR)                   0.001               0.001                   0.994
         Capitella.capitata Capitella.minima Chamelea.gallina Chironomidae.larvae
LR value             30.336            6.793           27.138               9.651
Pr(>LR)               0.002            0.718            0.002               0.396
         Cumella.limicola Cumella.pygmaea Cytharella.costulata Diogenes.pugilator
LR value           33.634           6.118                3.195              2.380
Pr(>LR)             0.001           0.804                0.983              0.991
         Eteone.flava Eunice.vittata Eurydice.dollfusi Exogone.naidina
LR value        4.159          3.572             6.118           7.227
Pr(>LR)         0.933          0.977             0.804           0.690
         Gastrosaccus.sanctus Genetyllis.tuberculata Glycera.sp. Glycera.tridactyla
LR value                2.773                  1.966       7.992              4.484
Pr(>LR)                 0.983                  0.994       0.575              0.925
         Glycera.unicornis Harmothoe.imbricata Harmothoe.reticulata
LR value             1.386               3.192                9.416
Pr(>LR)              0.994               0.983                0.421
         Heteromastus.filiformis Hirudinea Hydrobia.acuta Hydrobia.sp. Iphinoe.tenella
LR value                  17.463     1.726          1.438        2.250           5.470
Pr(>LR)                    0.027     0.994          0.994        0.991           0.869
         Kellia.suborbicularis Lagis.koreni Leiochone.leiopygos Lentidium.mediterraneum
LR value                 8.973       10.472              14.995                   5.545
Pr(>LR)                  0.469        0.312               0.077                   0.865
         Lepidochitona.cinerea Loripes.orbiculatus Lucinella.divaricata
LR value                 2.773              28.176                6.172
Pr(>LR)                  0.983               0.002                0.795
         Magelona.papillicornis Maldane.glebifex Melinna.palmata
LR value                  2.773            1.386          24.203
Pr(>LR)                   0.983            0.994           0.003
         Microdeutopus.gryllotalpa Micromaldane.ornithochaeta Micronephthys.stammeri
LR value                    13.747                      6.655                  2.773
Pr(>LR)                      0.113                      0.721                  0.983
         Microphthalmus.fragilis Microphthalmus.sp. Monocorophium.acherusicum
LR value                   1.437             11.855                    39.678
Pr(>LR)                    0.994              0.208                     0.001
         Mytilaster.lineatus Mytilus.galloprovincialis Nemertea Nephtys.cirrosa
LR value              34.910                     1.386    4.566           1.386
Pr(>LR)                0.001                     0.994    0.925           0.994
         Nephtys.kersivalensis Nereis.perivisceralis Nereis.pulsatoria
LR value                 1.386                 2.773             2.987
Pr(>LR)                  0.994                 0.983             0.983
         Nototropis.guttatus Oligochaeta Paradoneis.harpagonea Parthenina.interstincta
LR value               7.095      27.378                 1.386                   2.884
Pr(>LR)                0.690       0.002                 0.994                   0.983
         Parvicardium.exiguum Perinereis.cultrifera Perioculodes.longimanus Phoronida
LR value                2.911                 4.654                   4.365     5.372
Pr(>LR)                 0.983                 0.925                   0.925     0.879
         Phyllodoce.sp. Platyhelminthes Platynereis.dumerilii Polititapes.aureus
LR value          4.159           5.906                 8.537              4.065
Pr(>LR)           0.933           0.834                 0.523              0.943
         Polychaeta.larvae Polydora.ciliata Polygordius.neapolitanus
LR value             4.159           29.489                    4.159
Pr(>LR)              0.933            0.002                    0.933
         Prionospio.cirrifera Protodorvillea.kefersteini Pseudocuma.longicorne
LR value               41.351                     25.261                 1.726
Pr(>LR)                 0.001                      0.002                 0.994
         Rissoa.membranacea Rissoa.splendida Salvatoria.clavata Schistomeringos.rudolphi
LR value              1.701           17.118             32.959                    5.024
Pr(>LR)               0.994            0.032              0.001                    0.900
         Sphaerosyllis.hystrix Spio.filicornis Spisula.subtruncata Stenosoma.capito
LR value                12.736          34.632               5.885            7.189
Pr(>LR)                  0.154           0.001               0.834            0.690
         Syllis.gracilis Syllis.hyalina Tellina.tenuis Thracia.phaseolina
LR value          10.712          4.555          3.112              2.773
Pr(>LR)            0.306          0.925          0.983              0.983
         Tricolia.pullus Tritia.neritea Tritia.reticulata Turbellaria Upogebia.pusilla
LR value          13.288          2.037             2.932       1.527           10.026
Pr(>LR)            0.128          0.994             0.983       0.994            0.353
Arguments:
 Test statistics calculated assuming response assumed to be uncorrelated 
 P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).

The factor is highly significant according to the models.

Again, save the summary for safekeeping, but also run an anova.

write_rds(glms.lvm.zostera.3.summary, 
          here(save.dir, "glms_lvm_zostera_3_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.3.aov <- anova.manyglm(glms.lvm.zostera.3, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         pairwise.comp = ~lvm.clusters.zostera.3, ## check the pairwise comparisons between clusters
                                         show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.24 minutes...
    Resampling run 300 finished. Time elapsed: 0.37 minutes...
    Resampling run 400 finished. Time elapsed: 0.50 minutes...
    Resampling run 500 finished. Time elapsed: 0.63 minutes...
    Resampling run 600 finished. Time elapsed: 0.75 minutes...
    Resampling run 700 finished. Time elapsed: 0.88 minutes...
    Resampling run 800 finished. Time elapsed: 1.00 minutes...
    Resampling run 900 finished. Time elapsed: 1.13 minutes...
Time elapsed: 0 hr 1 min 15 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff   Dev Pr(>Dev)    
(Intercept)                31                           
lvm.clusters.zostera.3     28       3 965.7    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Pairwise comparison results: 
                                                     Observed statistic
lvm.clusters.zostera.3:2 vs lvm.clusters.zostera.3:3              368.1
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:3              355.8
lvm.clusters.zostera.3:2 vs lvm.clusters.zostera.3:4              336.6
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:2              319.4
lvm.clusters.zostera.3:3 vs lvm.clusters.zostera.3:4              295.1
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:4              275.0
                                                     Free Stepdown Adjusted P-Value   
lvm.clusters.zostera.3:2 vs lvm.clusters.zostera.3:3                          0.007 **
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:3                          0.007 **
lvm.clusters.zostera.3:2 vs lvm.clusters.zostera.3:4                          0.010 **
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:2                          0.010 **
lvm.clusters.zostera.3:3 vs lvm.clusters.zostera.3:4                          0.010 **
lvm.clusters.zostera.3:1 vs lvm.clusters.zostera.3:4                          0.010 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.3    27.438    0.002    4.159    1.000      1.386    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3          13.528    0.170            20.153    0.014
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3                  15.231    0.098        8.727    0.657
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3                 1.386    1.000              2.773    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                 51.414    0.001              34.189    0.001
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                   1.386    1.000             30.336    0.001
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3            6.793    0.868           27.138    0.002
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3               9.651    0.539           33.634    0.001
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3           6.118    0.940                3.195    1.000
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.3               2.38    1.000        4.159    1.000          3.572
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3    1.000             6.118    0.940           7.227    0.845
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3                2.773    1.000                  1.966    1.000
                       Glycera.sp.          Glycera.tridactyla         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.3       7.992    0.753              4.484    0.997
                       Glycera.unicornis          Harmothoe.imbricata         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3             1.386    1.000               3.192    1.000
                       Harmothoe.reticulata          Heteromastus.filiformis         
                                        Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.3                9.416    0.574                  17.463    0.039
                       Hirudinea          Hydrobia.acuta          Hydrobia.sp.         
                             Dev Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                            
lvm.clusters.zostera.3     1.726    1.000          1.438    1.000         2.25    1.000
                       Iphinoe.tenella          Kellia.suborbicularis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3            5.47    0.985                 8.973    0.633
                       Lagis.koreni          Leiochone.leiopygos         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.3       10.472    0.426              14.995    0.102
                       Lentidium.mediterraneum          Lepidochitona.cinerea         
                                           Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                   5.545    0.978                 2.773    1.000
                       Loripes.orbiculatus          Lucinella.divaricata         
                                       Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3              28.176    0.002                6.172    0.935
                       Magelona.papillicornis          Maldane.glebifex         
                                          Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.3                  2.773    1.000            1.386    1.000
                       Melinna.palmata          Microdeutopus.gryllotalpa         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.3          24.203    0.006                    13.747    0.156
                       Micromaldane.ornithochaeta          Micronephthys.stammeri
                                              Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
lvm.clusters.zostera.3                      6.655    0.888                  2.773
                                Microphthalmus.fragilis          Microphthalmus.sp.
                       Pr(>Dev)                     Dev Pr(>Dev)                Dev
(Intercept)                                                                        
lvm.clusters.zostera.3    1.000                   1.437    1.000             11.855
                                Monocorophium.acherusicum          Mytilaster.lineatus
                       Pr(>Dev)                       Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
lvm.clusters.zostera.3    0.280                    39.678    0.001               34.91
                                Mytilus.galloprovincialis          Nemertea         
                       Pr(>Dev)                       Dev Pr(>Dev)      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3    0.001                     1.386    1.000    4.566    0.996
                       Nephtys.cirrosa          Nephtys.kersivalensis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3           1.386    1.000                 1.386    1.000
                       Nereis.perivisceralis          Nereis.pulsatoria         
                                         Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.3                 2.773    1.000             2.987    1.000
                       Nototropis.guttatus          Oligochaeta         
                                       Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                             
lvm.clusters.zostera.3               7.095    0.848      27.378    0.002
                       Paradoneis.harpagonea          Parthenina.interstincta         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                 1.386    1.000                   2.884    1.000
                       Parvicardium.exiguum          Perinereis.cultrifera         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                2.911    1.000                 4.654    0.994
                       Perioculodes.longimanus          Phoronida         
                                           Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3                   4.365    0.997     5.372    0.987
                       Phyllodoce.sp.          Platyhelminthes         
                                  Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.3          4.159    1.000           5.906    0.946
                       Platynereis.dumerilii          Polititapes.aureus         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3                 8.537    0.673              4.065    1.000
                       Polychaeta.larvae          Polydora.ciliata         
                                     Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                
lvm.clusters.zostera.3             4.159    1.000           29.489    0.002
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                    4.159    1.000               41.351    0.001
                       Protodorvillea.kefersteini          Pseudocuma.longicorne
                                              Dev Pr(>Dev)                   Dev
(Intercept)                                                                     
lvm.clusters.zostera.3                     25.261    0.006                 1.726
                                Rissoa.membranacea          Rissoa.splendida         
                       Pr(>Dev)                Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.3    1.000              1.701    1.000           17.118    0.046
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3             32.959    0.001                    5.024    0.990
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3                12.736    0.208          34.632    0.001
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3               5.885    0.946            7.189    0.848
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                                                                           
lvm.clusters.zostera.3          10.712    0.392          4.555    0.996          3.112
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3    1.000              2.773    1.000          13.288    0.177
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                      <NA>     <NA>              <NA>     <NA>        <NA>
lvm.clusters.zostera.3          2.037    1.000             2.932    1.000       1.527
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                <NA>             <NA>     <NA>
lvm.clusters.zostera.3    1.000           10.026    0.466
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

According to the pairwise comparison, the case 3 clusters are significantly different from one another.. apparently sufficiently so.

Save the ANOVA, too.

write_rds(glms.lvm.zostera.3.aov, 
          here(save.dir, "glms_lvm_zostera_3_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.3 <- top_n_sp_glm(glms.lvm.zostera.3.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.82"
    Apseudopsis.ostroumovi       Prionospio.cirrifera  Monocorophium.acherusicum 
                 51.413970                  41.350974                  39.678240 
       Mytilaster.lineatus            Spio.filicornis        Bittium.reticulatum 
                 34.909870                  34.632433                  34.188511 
          Cumella.limicola         Salvatoria.clavata         Capitella.capitata 
                 33.633823                  32.958829                  30.336457 
          Polydora.ciliata        Loripes.orbiculatus                  Abra.alba 
                 29.489490                  28.175552                  27.437828 
               Oligochaeta           Chamelea.gallina Protodorvillea.kefersteini 
                 27.378351                  27.138297                  25.260955 
           Melinna.palmata          Ampelisca.diadema    Heteromastus.filiformis 
                 24.202974                  20.153373                  17.463258 
          Rissoa.splendida    Amphibalanus.improvisus        Leiochone.leiopygos 
                 17.117581                  15.231072                  14.994968 
 Microdeutopus.gryllotalpa            Alitta.succinea            Tricolia.pullus 
                 13.746930                  13.527612                  13.287785 
     Sphaerosyllis.hystrix         Microphthalmus.sp.            Syllis.gracilis 
                 12.736427                  11.854688                  10.711746 
              Lagis.koreni           Upogebia.pusilla        Chironomidae.larvae 
                 10.471907                  10.025894                   9.650905 
      Harmothoe.reticulata      Kellia.suborbicularis               Ampithoe.sp. 
                  9.416160                   8.973262                   8.726571 
     Platynereis.dumerilii                Glycera.sp.            Exogone.naidina 
                  8.536643                   7.992056                   7.227403 
          Stenosoma.capito        Nototropis.guttatus           Capitella.minima 
                  7.189015                   7.094867                   6.793482 
Micromaldane.ornithochaeta 
                  6.655076 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.3) <- names(top.sp.glms.lvm.zostera.3) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.3
    Apseudopsis ostroumovi       Prionospio cirrifera  Monocorophium acherusicum 
                 51.413970                  41.350974                  39.678240 
       Mytilaster lineatus            Spio filicornis        Bittium reticulatum 
                 34.909870                  34.632433                  34.188511 
          Cumella limicola         Salvatoria clavata         Capitella capitata 
                 33.633823                  32.958829                  30.336457 
          Polydora ciliata        Loripes orbiculatus                  Abra alba 
                 29.489490                  28.175552                  27.437828 
               Oligochaeta           Chamelea gallina Protodorvillea kefersteini 
                 27.378351                  27.138297                  25.260955 
           Melinna palmata          Ampelisca diadema    Heteromastus filiformis 
                 24.202974                  20.153373                  17.463258 
          Rissoa splendida    Amphibalanus improvisus        Leiochone leiopygos 
                 17.117581                  15.231072                  14.994968 
 Microdeutopus gryllotalpa            Alitta succinea            Tricolia pullus 
                 13.746930                  13.527612                  13.287785 
     Sphaerosyllis hystrix         Microphthalmus sp.            Syllis gracilis 
                 12.736427                  11.854688                  10.711746 
              Lagis koreni           Upogebia pusilla        Chironomidae larvae 
                 10.471907                  10.025894                   9.650905 
      Harmothoe reticulata      Kellia suborbicularis               Ampithoe sp. 
                  9.416160                   8.973262                   8.726571 
     Platynereis dumerilii                Glycera sp.            Exogone naidina 
                  8.536643                   7.992056                   7.227403 
          Stenosoma capito        Nototropis guttatus           Capitella minima 
                  7.189015                   7.094867                   6.793482 
Micromaldane ornithochaeta 
                  6.655076 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.3 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.3)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.3)))) %>% 
   mutate(group = factor(case_when(station %in% c("Poda", "Otmanli") ~ 1,
                                   station == "Vromos" ~ 2, 
                                   station == "Gradina" ~ 3, 
                                   station == "Ropotamo" ~ 4)) ## add the groups
          )
)
(plot.top.sp.glms.lvm.zostera.3 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.3,
                                              mapping = aes(x = species, y = log_y_min(count), colour = group),
                                              labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.3$group))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())
)

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.3 <- lapply(names(glms.lvm.zostera.3.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.3.summary, x, p = 0.05)) 
## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))
## rename columns (= group names) - right now they are something like "lvm.clusters.zostera3" etc.
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.3")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.3", "group_"))))
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))
## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.3 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1,
                           station == "Vromos" ~ 2, 
                           station == "Gradina" ~ 3, 
                           station == "Ropotamo" ~ 4)
         )
## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.3.smry <- zoo.abnd.zostera.long.3 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()
## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, zoo.abnd.zostera.long.3.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.3.smry %>% filter(group == .y) %>% unnest(), by = "species"))
## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, c(16, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
[[1]]

[[2]]

[[3]]

[[4]]
NA

In the case of the seagrasses and case 3 clusters, the picture is still more confusing..
The LRs seem to be a bit lower for groups 2 and 3, maybe 4 too - still not sure if you can use that as a significance measure.
For now, in group 1 (= Z1-Z2), the species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Oligochaeta, Heteromastus filiformis, Polydora ciliata, Prionosprio cirrifera, Rissoa membranacea, Abra alba, Ampelisca diadema (+ others, medium abundance); and the ones with a significantly lower abundance - or even absent - S. clavata, A. ostroumovi, C. gallina, T. pullus.
There are more species singled out for this cluster, probably because of the variability between the two years of sampling.
For group 2 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A. diadema. The species with lower abundance - in fact 0 - are B. reticulatum, P. cirrifera, S. clavata, A. alba, P. ciliata, oligochaetes, H. filiformis, R. splendida.
For group 3 (= Z4), the species with higher abundance are: M. lineatus, less so - C. limicola, L. orbiculatus, P. kefersteini, C. capitata, etc. The species with lower abundance (or 0) are: P. cirrifera, P. ciliata, A. alba, etc.
For group 4 (= Z5), the species with higher abundance are: A. ostoumovi, C. capitata, oligochaetes (very abundant, but with a small LR - nice!). The species with lower abundance (or 0) are: R. splendida, S. clavata, C. limicola.

All in all, I think that group 1 (Poda + Otmanli) holds, and so does group 2 (Vromos). The question is whether to separate Gradina and Ropotamo into 2 groups, or if they make more sense together. Ropotamo is characterized by a very high number of oligochaetes, while Gradina’s most distinguishing characteristic is the high number of M. lineatus - mostly very small ones, attached to the rhizomes, close to the sediment surface I presume. Both stations have C. limicola in medium abundance, a species that is not present anywhere else (is it?).

Try to compare the three models..

(glms.lvm.zostera.comp <- anova(glms.lvm.zostera.1,
                                glms.lvm.zostera.2, 
                                glms.lvm.zostera.3, 
                                p.uni = "adjusted")
)
Time elapsed: 0 hr 2 min 22 sec
Analysis of Deviance Table

glms.lvm.zostera.1: zoo.mvabnd.zostera ~ lvm.clusters.zostera.1
glms.lvm.zostera.3: zoo.mvabnd.zostera ~ lvm.clusters.zostera.3
glms.lvm.zostera.2: zoo.mvabnd.zostera ~ lvm.clusters.zostera.2

Multivariate test:
                   Res.Df Df.diff   Dev Pr(>Dev)    
glms.lvm.zostera.1     29                           
glms.lvm.zostera.3     28       1 262.1    0.001 ***
glms.lvm.zostera.2     27       1 256.8    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                   Abra.alba          Abra.sp.          Actiniaria         
                         Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
glms.lvm.zostera.1                                                         
glms.lvm.zostera.3     1.506    0.998        0    1.000          0    1.000
glms.lvm.zostera.2     0.023    1.000        0    1.000      1.386    1.000
                   Alitta.succinea          Ampelisca.diadema         
                               Dev Pr(>Dev)               Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3           4.881    0.681             0.094    1.000
glms.lvm.zostera.2          23.057    0.001            10.416    0.104
                   Amphibalanus.improvisus          Ampithoe.sp.         
                                       Dev Pr(>Dev)          Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3                   0.349    1.000        2.405    0.982
glms.lvm.zostera.2                   8.177    0.251        3.482    0.917
                   Anadara.kagoshimensis          Apherusa.bispinosa         
                                     Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                           
glms.lvm.zostera.3                     0    1.000              0.811    1.000
glms.lvm.zostera.2                 1.386    1.000                  0    1.000
                   Apseudopsis.ostroumovi          Bittium.reticulatum         
                                      Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3                 20.559    0.001               3.006    0.941
glms.lvm.zostera.2                   1.38    1.000               0.004    1.000
                   Brachynotus.sexdentatus          Capitella.capitata         
                                       Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3                   0.811    1.000              4.124    0.814
glms.lvm.zostera.2                   1.386    1.000              2.862    0.958
                   Capitella.minima          Chamelea.gallina         
                                Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3            6.055    0.518            0.908    1.000
glms.lvm.zostera.2            0.433    1.000            1.386    0.996
                   Chironomidae.larvae          Cumella.limicola         
                                   Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3               5.456    0.615            1.089    1.000
glms.lvm.zostera.2                   0    1.000            7.694    0.306
                   Cumella.pygmaea          Cytharella.costulata         
                               Dev Pr(>Dev)                  Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3           1.891    0.996                0.073    1.000
glms.lvm.zostera.2               0    1.000                4.159    0.834
                   Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                  Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3              1.483    0.999            0    1.000            2.7
glms.lvm.zostera.2               0.68    1.000            0    1.000          0.208
                            Eurydice.dollfusi          Exogone.naidina         
                   Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3    0.959             1.891    0.996           1.284    1.000
glms.lvm.zostera.2    1.000                 0    1.000            1.25    1.000
                   Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                    Dev Pr(>Dev)                    Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                0.811    1.000                  1.499    0.998
glms.lvm.zostera.2                    0    1.000                  5.746    0.574
                   Glycera.sp.          Glycera.tridactyla          Glycera.unicornis
                           Dev Pr(>Dev)                Dev Pr(>Dev)               Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3           0    1.000                  0    1.000                 0
glms.lvm.zostera.2           0    1.000              1.033    1.000             1.386
                            Harmothoe.imbricata          Harmothoe.reticulata         
                   Pr(>Dev)                 Dev Pr(>Dev)                  Dev Pr(>Dev)
glms.lvm.zostera.1                                                                    
glms.lvm.zostera.3    1.000               1.352    1.000                4.286    0.796
glms.lvm.zostera.2    1.000               5.561    0.595                5.794    0.566
                   Heteromastus.filiformis          Hirudinea          Hydrobia.acuta
                                       Dev Pr(>Dev)       Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3                   7.242    0.334     0.811    1.000              0
glms.lvm.zostera.2                  10.679    0.088         0    1.000          1.494
                            Hydrobia.sp.          Iphinoe.tenella         
                   Pr(>Dev)          Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                        
glms.lvm.zostera.3    1.000        0.569    1.000            1.31    1.000
glms.lvm.zostera.2    0.996        3.709    0.906           4.354    0.811
                   Kellia.suborbicularis          Lagis.koreni         
                                     Dev Pr(>Dev)          Dev Pr(>Dev)
glms.lvm.zostera.1                                                     
glms.lvm.zostera.3                 4.389    0.796        0.767    1.000
glms.lvm.zostera.2                 0.104    1.000        5.999    0.554
                   Leiochone.leiopygos          Lentidium.mediterraneum         
                                   Dev Pr(>Dev)                     Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3               8.777    0.194                   1.622    0.997
glms.lvm.zostera.2               0.336    1.000                       0    1.000
                   Lepidochitona.cinerea          Loripes.orbiculatus         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                            
glms.lvm.zostera.3                 0.811    1.000               2.917    0.948
glms.lvm.zostera.2                     0    1.000               3.172    0.936
                   Lucinella.divaricata          Magelona.papillicornis         
                                    Dev Pr(>Dev)                    Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                1.915    0.995                  0.811    1.000
glms.lvm.zostera.2                    0    1.000                      0    1.000
                   Maldane.glebifex          Melinna.palmata         
                                Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                   
glms.lvm.zostera.3                0    1.000               0    1.000
glms.lvm.zostera.2            1.386    0.999           2.657    0.983
                   Microdeutopus.gryllotalpa          Micromaldane.ornithochaeta
                                         Dev Pr(>Dev)                        Dev
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                    10.659    0.065                      2.111
glms.lvm.zostera.2                     2.603    0.984                          0
                            Micronephthys.stammeri          Microphthalmus.fragilis
                   Pr(>Dev)                    Dev Pr(>Dev)                     Dev
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3    0.995                  2.197    0.994                       0
glms.lvm.zostera.2    1.000                  1.386    1.000                   1.494
                            Microphthalmus.sp.          Monocorophium.acherusicum
                   Pr(>Dev)                Dev Pr(>Dev)                       Dev
glms.lvm.zostera.1                                                               
glms.lvm.zostera.3    1.000              2.459    0.979                      1.35
glms.lvm.zostera.2    0.996                  0    1.000                     0.213
                            Mytilaster.lineatus          Mytilus.galloprovincialis
                   Pr(>Dev)                 Dev Pr(>Dev)                       Dev
glms.lvm.zostera.1                                                                
glms.lvm.zostera.3    1.000              12.977    0.015                         0
glms.lvm.zostera.2    1.000              12.953    0.038                     1.386
                            Nemertea          Nephtys.cirrosa         
                   Pr(>Dev)      Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3    1.000    1.013    1.000           0.811    1.000
glms.lvm.zostera.2    1.000    5.479    0.634           1.386    1.000
                   Nephtys.kersivalensis          Nereis.perivisceralis         
                                     Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                     0    1.000                 0.811    1.000
glms.lvm.zostera.2                 1.386    1.000                     0    1.000
                   Nereis.pulsatoria          Nototropis.guttatus          Oligochaeta
                                 Dev Pr(>Dev)                 Dev Pr(>Dev)         Dev
glms.lvm.zostera.1                                                                    
glms.lvm.zostera.3                 0    1.000               4.485    0.751       5.602
glms.lvm.zostera.2             3.251    0.932               0.116    1.000       9.386
                            Paradoneis.harpagonea          Parthenina.interstincta
                   Pr(>Dev)                   Dev Pr(>Dev)                     Dev
glms.lvm.zostera.1                                                                
glms.lvm.zostera.3    0.607                     0    1.000                   0.919
glms.lvm.zostera.2    0.154                 1.386    1.000                   1.662
                            Parvicardium.exiguum          Perinereis.cultrifera         
                   Pr(>Dev)                  Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                      
glms.lvm.zostera.3    1.000                0.824    1.000                 0.973    1.000
glms.lvm.zostera.2    0.995                0.063    1.000                 2.035    0.992
                   Perioculodes.longimanus          Phoronida          Phyllodoce.sp.
                                       Dev Pr(>Dev)       Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3                   2.111    0.995     1.284    1.000              0
glms.lvm.zostera.2                       0    1.000      0.11    1.000              0
                            Platyhelminthes          Platynereis.dumerilii         
                   Pr(>Dev)             Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3    1.000           1.372    1.000                 1.257    1.000
glms.lvm.zostera.2    1.000           2.602    0.984                 0.374    1.000
                   Polititapes.aureus          Polychaeta.larvae         
                                  Dev Pr(>Dev)               Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3              0.751    1.000                 0    1.000
glms.lvm.zostera.2              6.933    0.404                 0    1.000
                   Polydora.ciliata          Polygordius.neapolitanus         
                                Dev Pr(>Dev)                      Dev Pr(>Dev)
glms.lvm.zostera.1                                                            
glms.lvm.zostera.3             13.8    0.012                        0    1.000
glms.lvm.zostera.2           12.416    0.045                        0    1.000
                   Prionospio.cirrifera          Protodorvillea.kefersteini         
                                    Dev Pr(>Dev)                        Dev Pr(>Dev)
glms.lvm.zostera.1                                                                  
glms.lvm.zostera.3               28.158    0.001                      7.725    0.294
glms.lvm.zostera.2                4.922    0.749                      4.879    0.749
                   Pseudocuma.longicorne          Rissoa.membranacea         
                                     Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                           
glms.lvm.zostera.3                 0.236    1.000              1.543    0.998
glms.lvm.zostera.2                 1.386    1.000              1.019    1.000
                   Rissoa.splendida          Salvatoria.clavata         
                                Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                      
glms.lvm.zostera.3            5.569    0.607             15.955    0.008
glms.lvm.zostera.2                0    1.000                  0    1.000
                   Schistomeringos.rudolphi          Sphaerosyllis.hystrix         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3                    2.389    0.982                 0.023    1.000
glms.lvm.zostera.2                    8.799    0.193                 4.024    0.863
                   Spio.filicornis          Spisula.subtruncata         
                               Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                      
glms.lvm.zostera.3           6.523    0.435                   0    1.000
glms.lvm.zostera.2           0.246    1.000                   0    1.000
                   Stenosoma.capito          Syllis.gracilis          Syllis.hyalina
                                Dev Pr(>Dev)             Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                  
glms.lvm.zostera.3            2.178    0.994           4.755    0.707          2.507
glms.lvm.zostera.2            6.661    0.472          17.831    0.008              0
                            Tellina.tenuis          Thracia.phaseolina         
                   Pr(>Dev)            Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3    0.979          1.622    0.997              0.811    1.000
glms.lvm.zostera.2    1.000          1.386    1.000                  0    1.000
                   Tricolia.pullus          Tritia.neritea          Tritia.reticulata
                               Dev Pr(>Dev)            Dev Pr(>Dev)               Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3           5.332    0.629          0.632    1.000                 0
glms.lvm.zostera.2            1.38    1.000          3.479    0.917             8.301
                            Turbellaria          Upogebia.pusilla         
                   Pr(>Dev)         Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                        
glms.lvm.zostera.3    1.000       1.392    0.999            5.769    0.566
glms.lvm.zostera.2    0.239       1.125    1.000                0    1.000
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Well this is tough to interpret.. Multivariate test table’s Dev is decrement from upper model, so each p-value indicates the difference between the model and upper one is statistically significant… But no info on which model represents the species matrix best.

I’ll go with the model with the lowest AIC, since there is no other objective criterion to go with.. This happens to be model 2 (groups = stations). Exactly the same result as from the classical methods.

glms.lvm.zostera.1$AICsum
[1] 6804.496
glms.lvm.zostera.2$AICsum
[1] 6661.507
glms.lvm.zostera.3$AICsum
[1] 6730.346
manyGLM by environmental parameters

Now, let’s try to see a different thing - which environmental parameters best describe the species response.
I’m going to use the PCA-filtered environmental data - it’s still going to be a slog, with 7 potential predictors..
First, construct the formula for the model - will do it separately in case I need to update it later, etc.
NB there is year here - I want to try with it first!! And I don’t want the Secchi depth - it has NAs for Vromos.

(formula.env.glms.zostera <- formula(paste("zoo.mvabnd.zostera ~",
                                           paste(env.zostera %>% select(-c(station, secchi)) %>% names(), collapse = "+")))
)
zoo.mvabnd.zostera ~ year + Ntotal + chl_a + LUSI + TOM + moisture_content + 
    mean_grain_size + sand + silt_clay + shoot_count + ag_biomass_wet + 
    bg_biomass_wet

Fit the GLMs - including all environmental parameters - to the zostera abundance data.

env.glms.zostera <- manyglm(formula.env.glms.zostera,
                            data = env.zostera,
                            family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(env.glms.zostera)

## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.zostera, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

Well, it’s good enough if you ask me (still the kinda strange “line” at lin.pred = -6; otherwise residuals are random enough).

Save the model!

write_rds(env.glms.zostera, 
          here(save.dir, "glms_env_zostera.RDS"))

Before going off and running an ANOVA to check which predictors best explain the species abundance patterns, I’ll try to reduce the model a little - it might even improve the fit, not to mention the run time.

top.env.glm.red.zostera <- evaluate_glms_env(env.glms.zostera)
the condition has length > 1 and only the first element will be used
[1] "Best model:  zoo.mvabnd.zostera ~ Ntotal + sand + shoot_count + ag_biomass_wet +     bg_biomass_wet"

Check its fit.

## residuals vs fitted values
plot(top.env.glm.red.zostera)



## all traditional (g)lm diagnostic plots
plot.manyglm(top.env.glm.red.zostera, which = 1:3)

I think it’s fine; might even be better than the full model.. Save it, too.

write_rds(top.env.glm.red.zostera, 
          here(save.dir, "glms_top_env_red_zostera.RDS"))

Save the diagnostic plots.

png(here(figures.dir, "diagnostic_top_glm_env_red_zostera.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(top.env.glm.red.zostera, which = 1:3)
dev.off()
null device 
          1 

Run ANOVA on this model.

(top.env.glm.red.zostera.aov <- anova.manyglm(top.env.glm.red.zostera,
                                              test = "LR", p.uni = "adjusted", 
                                              nBoot = 999, ## limit the number of permutations for a shorter run time   
                                              show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
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Resampling begins for test 2.
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Resampling begins for test 3.
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Resampling begins for test 4.
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Resampling begins for test 5.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
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    Resampling run 800 finished. Time elapsed: 0.98 minutes...
    Resampling run 900 finished. Time elapsed: 1.11 minutes...
Time elapsed: 0 hr 6 min 45 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ Ntotal + sand + shoot_count + 
Model:     ag_biomass_wet + bg_biomass_wet, family = "negative.binomial", 
Model:     data = env.zostera)

Multivariate test:
               Res.Df Df.diff   Dev Pr(>Dev)    
(Intercept)        31                           
Ntotal             30       1 299.7    0.001 ***
sand               29       1 272.1    0.001 ***
shoot_count        28       1 355.3    0.001 ***
ag_biomass_wet     27       1 235.2    0.001 ***
bg_biomass_wet     26       1 424.9    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
               Abra.alba          Abra.sp.          Actiniaria          Alitta.succinea
                     Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)             Dev
(Intercept)                                                                            
Ntotal             6.177    0.545    4.157    0.945      1.004    1.000          19.751
sand               19.42    0.004        0    1.000      0.412    1.000           0.204
shoot_count        0.506    1.000    0.002    1.000      2.581    0.999           1.336
                        Ampelisca.diadema          Amphibalanus.improvisus         
               Pr(>Dev)               Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                        
Ntotal            0.003             5.846    0.578                  10.874    0.057
sand              1.000            25.503    0.002                   1.185    1.000
shoot_count       1.000            27.113    0.001                   0.224    1.000
               Ampithoe.sp.          Anadara.kagoshimensis          Apherusa.bispinosa
                        Dev Pr(>Dev)                   Dev Pr(>Dev)                Dev
(Intercept)                                                                           
Ntotal               10.408    0.080                 1.004    0.999               0.83
sand                  1.162    1.000                 0.381    1.000              3.329
shoot_count            0.23    1.000                 2.765    0.995                  0
                        Apseudopsis.ostroumovi          Bittium.reticulatum         
               Pr(>Dev)                    Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                         
Ntotal            1.000                  5.466    0.634               1.145    0.999
sand              0.981                  5.211    0.802               0.291    1.000
shoot_count       1.000                 10.604    0.169              18.053    0.006
               Brachynotus.sexdentatus          Capitella.capitata         
                                   Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                
Ntotal                           0.004    1.000              1.871    0.998
sand                             0.202    1.000              1.595    0.999
shoot_count                      0.445    1.000              15.66    0.019
               Capitella.minima          Chamelea.gallina          Chironomidae.larvae
                            Dev Pr(>Dev)              Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
Ntotal                    1.126    0.999            0.789    1.000               9.648
sand                      0.223    1.000            3.252    0.986                   0
shoot_count              20.087    0.003           12.142    0.098               0.001
                        Cumella.limicola          Cumella.pygmaea         
               Pr(>Dev)              Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                               
Ntotal            0.162            0.501    1.000             2.1    0.996
sand              1.000            2.908    0.992            7.78    0.433
shoot_count       1.000            3.986    0.934           0.001    1.000
               Cytharella.costulata          Diogenes.pugilator          Eteone.flava
                                Dev Pr(>Dev)                Dev Pr(>Dev)          Dev
(Intercept)                                                                          
Ntotal                        0.849    1.000              0.003    1.000        4.157
sand                          0.163    1.000              0.317    1.000            0
shoot_count                    0.48    1.000              6.108    0.672        0.002
                        Eunice.vittata          Eurydice.dollfusi         
               Pr(>Dev)            Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
Ntotal            0.940          3.083    0.990               2.1    0.996
sand              1.000          3.191    0.988             7.638    0.449
shoot_count       1.000          0.665    1.000             0.142    1.000
               Exogone.naidina          Gastrosaccus.sanctus         
                           Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                          
Ntotal                   7.771    0.381                 0.83    1.000
sand                     3.266    0.986                3.329    0.976
shoot_count              0.698    1.000                    0    1.000
               Genetyllis.tuberculata          Glycera.sp.          Glycera.tridactyla
                                  Dev Pr(>Dev)         Dev Pr(>Dev)                Dev
(Intercept)                                                                           
Ntotal                          1.232    0.999       1.097    0.999              0.066
sand                            6.164    0.679       4.521    0.887              2.045
shoot_count                     3.149    0.976       0.675    1.000              8.534
                        Glycera.unicornis          Harmothoe.imbricata         
               Pr(>Dev)               Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                    
Ntotal            1.000             1.004    1.000               0.915    1.000
sand              0.999             0.381    1.000               6.699    0.595
shoot_count       0.342             2.765    0.996              10.277    0.192
               Harmothoe.reticulata          Heteromastus.filiformis          Hirudinea
                                Dev Pr(>Dev)                     Dev Pr(>Dev)       Dev
(Intercept)                                                                            
Ntotal                        2.036    0.997                   2.133    0.996         0
sand                          8.582    0.320                   4.357    0.912     0.091
shoot_count                   0.077    1.000                   1.732    1.000     0.014
                        Hydrobia.acuta          Hydrobia.sp.          Iphinoe.tenella
               Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)             Dev
(Intercept)                                                                          
Ntotal            1.000          1.425    0.999        1.301    0.999           0.144
sand              1.000          0.408    1.000        0.215    1.000           3.241
shoot_count       1.000          2.507    0.999        0.013    1.000           0.005
                        Kellia.suborbicularis          Lagis.koreni         
               Pr(>Dev)                   Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                 
Ntotal            1.000                 2.726    0.990            0    1.000
sand              0.986                 1.702    0.999        2.559    0.996
shoot_count       1.000                 8.058    0.409       11.219    0.140
               Leiochone.leiopygos          Lentidium.mediterraneum         
                               Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                 
Ntotal                       2.493    0.992                   1.659    0.999
sand                          1.08    1.000                   6.526    0.645
shoot_count                  7.538    0.473                   0.131    1.000
               Lepidochitona.cinerea          Loripes.orbiculatus         
                                 Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                               
Ntotal                          0.83    1.000               1.634    0.999
sand                           3.215    0.988               1.236    1.000
shoot_count                    0.113    1.000              22.136    0.001
               Lucinella.divaricata          Magelona.papillicornis         
                                Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                 
Ntotal                        2.519    0.992                   0.83    1.000
sand                          0.005    1.000                  3.215    0.988
shoot_count                   3.884    0.942                  0.113    1.000
               Maldane.glebifex          Melinna.palmata         
                            Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                      
Ntotal                    1.004    0.999           3.974    0.966
sand                      0.412    1.000           1.826    0.999
shoot_count               2.581    0.999            5.31    0.810
               Microdeutopus.gryllotalpa          Micromaldane.ornithochaeta         
                                     Dev Pr(>Dev)                        Dev Pr(>Dev)
(Intercept)                                                                          
Ntotal                             5.334    0.664                      4.195    0.900
sand                               1.148    1.000                      6.449    0.655
shoot_count                         3.03    0.981                          0    1.000
               Micronephthys.stammeri          Microphthalmus.fragilis         
                                  Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                    
Ntotal                          3.828    0.970                    0.03    1.000
sand                            0.614    1.000                   1.905    0.999
shoot_count                     1.079    1.000                   2.619    0.998
               Microphthalmus.sp.          Monocorophium.acherusicum         
                              Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                  
Ntotal                      1.497    0.999                    14.561    0.019
sand                        0.028    1.000                     0.234    1.000
shoot_count                 4.309    0.932                    18.824    0.005
               Mytilaster.lineatus          Mytilus.galloprovincialis          Nemertea
                               Dev Pr(>Dev)                       Dev Pr(>Dev)      Dev
(Intercept)                                                                            
Ntotal                       15.75    0.012                     1.004    0.999    0.617
sand                         1.073    1.000                     0.381    1.000    0.254
shoot_count                  5.489    0.792                     2.765    0.995      9.1
                        Nephtys.cirrosa          Nephtys.kersivalensis         
               Pr(>Dev)             Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                    
Ntotal            1.000           0.458    1.000                 1.004    1.000
sand              1.000           0.059    1.000                 0.381    1.000
shoot_count       0.288           1.444    1.000                 2.765    0.996
               Nereis.perivisceralis          Nereis.pulsatoria         
                                 Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                             
Ntotal                          0.83    1.000             2.909    0.990
sand                           3.329    0.976             0.077    1.000
shoot_count                        0    1.000             0.002    1.000
               Nototropis.guttatus          Oligochaeta          Paradoneis.harpagonea
                               Dev Pr(>Dev)         Dev Pr(>Dev)                   Dev
(Intercept)                                                                           
Ntotal                       4.526    0.882       5.007    0.722                 1.004
sand                         1.555    0.999       1.836    0.999                 0.412
shoot_count                  4.117    0.932      12.359    0.089                 2.581
                        Parthenina.interstincta          Parvicardium.exiguum         
               Pr(>Dev)                     Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
Ntotal            1.000                   1.009    0.999                2.023    0.997
sand              1.000                   0.001    1.000                0.537    1.000
shoot_count       0.999                  10.718    0.169                2.433    0.999
               Perinereis.cultrifera          Perioculodes.longimanus          Phoronida
                                 Dev Pr(>Dev)                     Dev Pr(>Dev)       Dev
(Intercept)                     <NA>     <NA>                    <NA>     <NA>      <NA>
Ntotal                         2.475    0.992                   0.055    1.000     0.004
sand                           1.989    0.999                   0.003    1.000     2.218
shoot_count                     0.04    1.000                   5.602    0.769      4.34
                        Phyllodoce.sp.          Platyhelminthes         
               Pr(>Dev)            Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)        <NA>           <NA>     <NA>            <NA>     <NA>
Ntotal            1.000          4.157    0.940           1.998    0.997
sand              0.998              0    1.000               0    1.000
shoot_count       0.928          0.002    1.000           0.742    1.000
               Platynereis.dumerilii          Polititapes.aureus         
                                 Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                     <NA>     <NA>               <NA>     <NA>
Ntotal                         1.236    0.999              0.241    1.000
sand                           0.216    1.000              6.606    0.624
shoot_count                     6.46    0.620              1.073    1.000
               Polychaeta.larvae          Polydora.ciliata         
                             Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                 <NA>     <NA>             <NA>     <NA>
Ntotal                     4.157    0.937           25.833    0.001
sand                           0    1.000           10.787    0.131
shoot_count                0.002    1.000            4.281    0.932
               Polygordius.neapolitanus          Prionospio.cirrifera         
                                    Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                        <NA>     <NA>                 <NA>     <NA>
Ntotal                            4.157    0.937                3.887    0.967
sand                                  0    1.000               48.848    0.001
shoot_count                       0.002    1.000                0.005    1.000
               Protodorvillea.kefersteini          Pseudocuma.longicorne         
                                      Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                          <NA>     <NA>                  <NA>     <NA>
Ntotal                              5.159    0.708                 0.884    1.000
sand                                0.994    1.000                 2.017    0.999
shoot_count                          0.73    1.000                 0.192    1.000
               Rissoa.membranacea          Rissoa.splendida          Salvatoria.clavata
                              Dev Pr(>Dev)              Dev Pr(>Dev)                Dev
(Intercept)                  <NA>     <NA>             <NA>     <NA>               <NA>
Ntotal                      2.146    0.996            0.416    1.000              1.798
sand                        3.924    0.953            3.515    0.964              2.994
shoot_count                 0.204    1.000             1.17    1.000              0.118
                        Schistomeringos.rudolphi          Sphaerosyllis.hystrix         
               Pr(>Dev)                      Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)        <NA>                     <NA>     <NA>                  <NA>     <NA>
Ntotal            0.999                    1.251    0.999                 0.109    1.000
sand              0.991                    1.657    0.999                 0.151    1.000
shoot_count       1.000                     9.19    0.284                10.018    0.223
               Spio.filicornis          Spisula.subtruncata          Stenosoma.capito
                           Dev Pr(>Dev)                 Dev Pr(>Dev)              Dev
(Intercept)               <NA>     <NA>                <NA>     <NA>             <NA>
Ntotal                  17.283    0.007               0.014    1.000             1.53
sand                     0.075    1.000               0.081    1.000            4.409
shoot_count              5.161    0.847                3.58    0.961             0.02
                        Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
               Pr(>Dev)             Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)        <NA>            <NA>     <NA>           <NA>     <NA>           <NA>
Ntotal            0.999           3.343    0.986          4.551    0.882          1.144
sand              0.901           0.432    1.000              0    1.000          1.096
shoot_count       1.000           1.132    1.000          0.001    1.000          2.189
                        Thracia.phaseolina          Tricolia.pullus         
               Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)        <NA>               <NA>     <NA>            <NA>     <NA>
Ntotal            0.999               0.83    1.000           3.903    0.967
sand              1.000              3.329    0.981           0.445    1.000
shoot_count       0.999                  0    1.000           0.012    1.000
               Tritia.neritea          Tritia.reticulata          Turbellaria         
                          Dev Pr(>Dev)               Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)              <NA>     <NA>              <NA>     <NA>        <NA>     <NA>
Ntotal                  0.972    1.000             0.049    1.000        0.01    1.000
sand                    0.698    1.000             5.174    0.808       0.763    1.000
shoot_count             0.444    1.000             0.182    1.000       0.158    1.000
               Upogebia.pusilla         
                            Dev Pr(>Dev)
(Intercept)                <NA>     <NA>
Ntotal                   10.023    0.128
sand                          0    1.000
shoot_count               0.001    1.000
 [ reached getOption("max.print") -- omitted 2 rows ]
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Nice, all terms are significant now! Again, as with the sand samples, there is one eutrophication term + one sediment composition + seagrass parameters. Seems reasonable enough.

Save this ANOVA (takes too long to run anew).

write_rds(top.env.glm.red.zostera.aov, 
          here(save.dir, "glms_top_env_red_zostera_anova.RDS"))

Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).

## get the top contributing species for the environmental parameter zostera GLMs 
(top.sp.glms.env.red.zostera <- top_n_sp_glm(top.env.glm.red.zostera.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.771"
          Polydora.ciliata            Alitta.succinea            Spio.filicornis 
                 25.833258                  19.750751                  17.282878 
       Mytilaster.lineatus  Monocorophium.acherusicum    Amphibalanus.improvisus 
                 15.750298                  14.561059                  10.874348 
              Ampithoe.sp.           Upogebia.pusilla        Chironomidae.larvae 
                 10.407890                  10.022548                   9.647785 
           Exogone.naidina                  Abra.alba          Ampelisca.diadema 
                  7.770666                   6.177181                   5.846268 
    Apseudopsis.ostroumovi  Microdeutopus.gryllotalpa Protodorvillea.kefersteini 
                  5.466183                   5.334367                   5.159364 
               Oligochaeta             Syllis.hyalina        Nototropis.guttatus 
                  5.007334                   4.551098                   4.525633 
Micromaldane.ornithochaeta          Polychaeta.larvae   Polygordius.neapolitanus 
                  4.195233                   4.157056                   4.157056 
              Eteone.flava             Phyllodoce.sp.                   Abra.sp. 
                  4.157056                   4.157056                   4.157056 
           Melinna.palmata            Tricolia.pullus       Prionospio.cirrifera 
                  3.974488                   3.902948                   3.886516 
    Micronephthys.stammeri            Syllis.gracilis             Eunice.vittata 
                  3.827638                   3.343254                   3.082611 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   DON'T BE IN A HURRY TO DO THAT IF YOU WANT TO SUBSET THE ORIGINAL MATRIX BEFORE RUNNING TRAITGLM 
names(top.sp.glms.env.red.zostera) <- names(top.sp.glms.env.red.zostera) %>% 
  str_replace(pattern = "\\.", replacement = " ")

I’m going to plot these top contributing species, but I’m not using the plot. At least this time it’s more manageable, but still not presentable enough..

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.env.red.zostera <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.env.red.zostera)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.env.red.zostera)))) %>% 
   ## add clusters from LVM as a column
   mutate(group = case_when(station == "Poda" ~ 1, 
                            station == "Otmanli" ~ 2, 
                            station == "Vromos" ~ 3, 
                            station == "Gradina" ~ 4, 
                            station == "Ropotamo" ~ 5))
)
(plot.top.sp.glms.env.red.zostera <- plot_top_n(abnd.top.sp.glms.env.red.zostera,
                                         mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                         labs.legend = unique(abnd.top.sp.glms.env.red.zostera$group),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) + 
    theme(legend.position = "top")
)

Extract the taxon information (univariate tests) from the model ANOVA to present as a table (probably better than this plot, although it’s informative).

## extract the univariate test coefficients (LR) from the environmental model ANOVA. NB keep the row names when converting the matrix to tibble! 
table.top.sp.glms.env.red.zostera <- as_tibble(top.env.glm.red.zostera.aov$uni.test, rownames = "var")
## fix the species names - remove first dor  
names(table.top.sp.glms.env.red.zostera) <- names(table.top.sp.glms.env.red.zostera) %>% 
  str_replace(pattern = "\\.", replacement = " ")
## subset only the top species (explaining ~75% of the dataset variation)
table.top.sp.glms.env.red.zostera <- table.top.sp.glms.env.red.zostera %>% 
  select(var, names(top.sp.glms.env.red.zostera))
## transpose, because a table with 50 columns is just unreadable
(table.top.sp.glms.env.red.zostera <- table.top.sp.glms.env.red.zostera %>%
    gather(key = species, value = value, -var) %>% 
    spread(key = var, value = value) %>% 
    ## arrange as before (terms in the order they appear in the model, and by descending value of the LR for the first model term - here, PO4). Also get rid of the intercept (it's all-NA anyway).
    select(species, Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet) %>%
    arrange(desc(Ntotal)) 
)

Save this to a file - will have to format it as a nice table by hand, unfortunately.

write_csv(table.top.sp.glms.env.red.zostera, 
          here(save.dir, "taxa_contrib_glms_top_env_red_zostera.csv"))

Calculate the percentage contribution of each of these species to each of the model terms (Dev(term) = Sum-of-LR - sum of the LRs for the individual univariate species tests)..

## get the total deviance (Sum-of-LR) for each model term
(dev.terms.top.glms.env.zostera <- as_tibble(top.env.glm.red.zostera.aov$table, rownames = "var") %>%
   ## get rid of unnecessary variables (I only want the deviance value for each term) and intercept term 
   select(var, Dev) %>% 
   filter(var != "(Intercept)") %>% 
   ## transpose 
   gather(variable, value, -var) %>%
   spread(var, value) %>% 
   ## get rid of first column and rearrange columns to match table of deviances of univariate tests for species 
   select(-variable) %>% 
   select(Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet)
)  
## calculate the proportion contribution of each species to each parameter deviance
prop.top.sp.glms.env.red.zostera <- map2_df(table.top.sp.glms.env.red.zostera %>% select(-species), 
                                            dev.terms.top.glms.env.zostera,
                                            ~.x/.y)
## add back the species 
(prop.top.sp.glms.env.red.zostera <- bind_cols(table.top.sp.glms.env.red.zostera %>% select(species), 
                                               prop.top.sp.glms.env.red.zostera)
)

I’ll do the pseudo-traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix), although I don’t think it will amount to anything useful.
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.

sp.response.glms.env.red.zostera <- traitglm(L = mvabund(zoo.abnd.flt.zostera[, names(top.sp.glms.env.red.zostera)]), 
                                             R = as.matrix(env.zostera %>% select(Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet)), 
                                             method = "manyglm")
No traits matrix entered, so will fit SDMs with different env response for each spp 
sp.response.glms.env.red.zostera$fourth.corner
                                        Ntotal          sand shoot_count ag_biomass_wet
names.L.Abra.sp.                   -0.47066762  0.8734886154  0.46922359    -0.19993821
names.L.Alitta.succinea             0.97052617  0.9239972975  0.15761977     0.34540391
names.L.Ampelisca.diadema           0.07926714  0.4982502059  0.08427469     0.04139468
names.L.Amphibalanus.improvisus     0.01579908  0.1367386026  0.02102261    -0.02672181
names.L.Ampithoe.sp.               -0.23185028  0.9766780527 -0.86628249    -0.74571356
names.L.Apseudopsis.ostroumovi      1.64548321 -1.0408187107 -1.81840977     0.56715226
names.L.Chironomidae.larvae         1.31227261  0.1002162364  0.12598021     0.05010550
names.L.Eteone.flava               -0.47066762  0.8734886147  0.46922359    -0.19993821
names.L.Eunice.vittata             -0.80681453 -1.1651097143  0.87652213     0.87742696
names.L.Exogone.naidina            -2.71929348 -1.2204528999  0.50458742     0.72444467
names.L.Melinna.palmata            -0.60638932  0.1355595122  0.47942801    -0.75972197
names.L.Microdeutopus.gryllotalpa  -0.06793176  0.1548066634  0.05529672     0.15492252
names.L.Micromaldane.ornithochaeta -0.03794287  1.1454709967  0.21794177    -0.18913046
names.L.Micronephthys.stammeri     -0.27494238 -0.3866591307  0.52525177     1.09138609
names.L.Monocorophium.acherusicum  -0.17196470  0.2856739339  0.13559306    -0.02596581
names.L.Mytilaster.lineatus        -0.12863711  0.0415408498 -0.21351554     0.13096055
names.L.Nototropis.guttatus        -3.39299319 -2.6671597928  1.95831019     2.81907411
names.L.Oligochaeta                 0.24580986  0.0008031048 -0.27535910     0.05999869
names.L.Phyllodoce.sp.             -0.47066762  0.8734886150  0.46922359    -0.19993821
names.L.Polychaeta.larvae          -0.47066762  0.8734886136  0.46922359    -0.19993820
names.L.Polydora.ciliata            0.08423213  0.0097291405  0.15937837     0.02005751
names.L.Polygordius.neapolitanus   -0.47066762  0.8734886143  0.46922359    -0.19993821
names.L.Prionospio.cirrifera        0.88939049 -0.8247531556 -0.04010420    -0.33490099
names.L.Protodorvillea.kefersteini -2.59810569 -2.3545060528  0.75998659     2.29012099
names.L.Spio.filicornis            -0.38562919  0.2369199100  0.06576463    -0.07758304
names.L.Syllis.gracilis             0.70617192 -1.4267780844 -1.03624608     0.23992203
names.L.Syllis.hyalina              1.41675539  0.0868009271  0.13451699     0.04413407
names.L.Tricolia.pullus            -0.66341187 -2.5031380589 -0.53076627     1.42443911
names.L.Upogebia.pusilla            1.37595789  0.0920536483  0.13121625     0.04647257
                                   bg_biomass_wet
names.L.Abra.sp.                      -0.25357886
names.L.Alitta.succinea               -0.76895635
names.L.Ampelisca.diadema              0.18259939
names.L.Amphibalanus.improvisus       -0.23201790
names.L.Ampithoe.sp.                   0.03055559
names.L.Apseudopsis.ostroumovi         1.74812763
names.L.Chironomidae.larvae            1.03836845
names.L.Eteone.flava                  -0.25357886
names.L.Eunice.vittata                 0.52390238
names.L.Exogone.naidina                0.09265243
names.L.Melinna.palmata               -1.53484185
names.L.Microdeutopus.gryllotalpa      0.19540154
names.L.Micromaldane.ornithochaeta     0.50432844
names.L.Micronephthys.stammeri         0.19869790
names.L.Monocorophium.acherusicum      0.03209065
names.L.Mytilaster.lineatus            0.41368623
names.L.Nototropis.guttatus            1.74403783
names.L.Oligochaeta                    0.37862412
names.L.Phyllodoce.sp.                -0.25357886
names.L.Polychaeta.larvae             -0.25357886
names.L.Polydora.ciliata              -0.18809997
names.L.Polygordius.neapolitanus      -0.25357886
names.L.Prionospio.cirrifera          -0.11604329
names.L.Protodorvillea.kefersteini     1.48926441
names.L.Spio.filicornis               -0.32857846
names.L.Syllis.gracilis                1.78601308
names.L.Syllis.hyalina                 1.10641092
names.L.Tricolia.pullus                2.08730622
names.L.Upogebia.pusilla               1.07984888
# plot this 
a.z <- max(abs(sp.response.glms.env.red.zostera$fourth.corner))
colort <- colorRampPalette(c("blue","white","red")) 
plot.spp.z <- lattice::levelplot(t(as.matrix(sp.response.glms.env.red.zostera$fourth.corner)), xlab = "Environmental Variables",
                     ylab = "Species", col.regions = colort(100), at = seq(-a.z, a.z, length = 100),
                     scales = list(x = list(rot = 45)))
print(plot.spp.z)

Here at least the directions are a little more coherent than the environmental parameters for the sand stations (seagrass biomasses more or less in the same direction, etc.). The below-ground biomass exerts more pronounced influence on the specific abundances - normal, since most of these are infauna.

---
title: "Multivariate analyses of community structure (modeling)"
date: "`r Sys.Date()`"
output: html_notebook
---

This notebook contains all multivariate analyses of zoobenthic community structure using the new, nearly unheard-of modeling methods: packages mvabund, boral.  
Again, to make it self-contained, there will be the same repetitive setup/data import/preparation part.  

***  

Setup!
```{r setup, include = FALSE}
library(knitr)

knit_hooks$set(small.mar = function(before, options, envir) {
    if (before) par(mar = c(2, 2, .1, 2))  # smaller margin on top
})

## set the working directory to one up (all notebooks - kept in their own subdirectory within the project directory).
opts_knit$set(root.dir = rprojroot::find_rstudio_root_file())

## set knitr options for knitting code into the report.
opts_chunk$set(cache = TRUE, # save results so that code blocks aren't re-run unless code changes
               autodep = TRUE, # ..or unless a relevant earlier code block changed
               cache.comments = FALSE, # don't re-run if the only thing that changed was the comments
               highlight = TRUE, 
               small.mar = TRUE)
```

Define the working subdirectories.  
```{r workspace_setup}
## print the working directory, just to be on the safe side
paste("You are here: ", getwd())

data.dir <- "data"    ## input data files
functions.dir <- "R"  ## functions & scripts
save.dir <- "output"  ## clean data, output from models & more complex calculations
figures.dir <- "figs" ## plots & figures 
```

Import libraries.  
```{r import_packages, results = FALSE}
library(here) ## painless relative paths to subdurectories, etc.
library(tidyverse) ## data manipulation, cleaning, aggregation
library(viridis) ## smart & pretty colour schemes
library(mvabund) ## multivariate modeling analyses in ecology
library(boral) ## more multivariate modeling analyses in ecology
```

Organize some commonly-used ggplot2 modifications into a more convenient (and less repetitive) format. One day, I MUST figure out the proper way to set the theme..    
```{r custom_ggplot_settings_helpers}
## ggplot settings & things that I keep reusing
# ggplot_theme <- list(
#   theme_bw(),
#   theme(element_text(family = "Times"))
# )

## always use black-and-white theme
theme_set(theme_bw())

## helper to adjust ggplot text size & avoid repetitions 
text_size <- function(text.x = NULL,
                      text.y = NULL,
                      title.x = NULL,
                      title.y = NULL,
                      legend.text = NULL,
                      legend.title = NULL, 
                      strip.x = NULL, 
                      strip.y = NULL) {
  theme(axis.text.x = element_text(size = text.x),
        axis.text.y = element_text(size = text.y),
        axis.title.x = element_text(size = title.x),
        axis.title.y = element_text(size = title.y),
        legend.text = element_text(size = legend.text), 
        legend.title = element_text(size = legend.title), 
        strip.text.x = element_text(size = strip.x), 
        strip.text.y = element_text(size = strip.y)
        )
}


## log y/min + 1 transform - useful for species counts/biomass data visualization
log_y_min <- function(y) {
  log(y / min(y[y > 0]) + 1)
}

```

***  

#### **Sand stations (Burgas Bay, 2013-2014)**  
Import zoobenthic abundance data (cleaned and prepared).  
```{r import_zoo_abnd_sand}
zoo.abnd.sand <- read_csv(here(save.dir, "abnd_sand_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.sand <- zoo.abnd.sand %>% 
    mutate(station = factor(station, levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)
```

Remove the all-0 species (= not present in the current dataset).  
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it's unlikely they carry important information, but it would probably improve the run times).  
```{r filter_zoo_data_sand}
(zoo.abnd.flt.sand <- zoo.abnd.sand %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
```


##### **LVM - model-based ordination**
Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.   
I'm including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of **species composition**.   
NB this takes about a million years to run! 
```{r lvm_sand}
lvm.sand <- boral(y = zoo.abnd.flt.sand, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:6, each = 9), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

```

Check the summary and diagnostic plots for the LVM.  
```{r summary_lvm_sand}
summary(lvm.sand)

## model fit diagnostic plots
plot(lvm.sand)
```
The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a normal distribution of the residuals) - the model fits the data pretty well.  

Save the sand LVM.  
```{r save_lvm_sand}
write_rds(lvm.sand, 
          here(save.dir, "lvm_sand.RDS"))
```

Save the diagnostic plots.  
```{r save_diagn_plots_lvm_sand}
png(here(figures.dir, "diagnostic_lvm_sand.png"), width = 25, height = 20, units = "cm", res = 300)
par(mfrow = c(2, 2))
plot(lvm.sand)
par(mfrow = c(1, 1))
dev.off()
```



Examine the biplot obtained by fitting the LVM, as well as the 20 most "important" species.   
```{r check_biplot_lvm_sand}
lvsplot(lvm.sand, jitter = T, biplot = TRUE, ind.spp = 20)
```

All in all, the final result resembles the nMDS ordination very much - same 4 clusters (Kraimorie + Chukalya, AKin, Agalina, Sozopol + Paraskeva). Kraimorie and Chukalya are better distinguished on the LVM plot than on the MDS, but still.  
The run time is extremely, extremely long (~1h), but the data don't need to be transformed, and the model fit can be examined and adjusted if necessary.    
The species singled out as significant are probably somewhat different - have to check!   

Redo the biplot, because this one is not very pretty. I'm not adding the species on top, first because I'm too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.   
```{r extract_lvm_coord_sand}
## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.sand <- as_tibble(lvm.sand$lv.median)

## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.sand <- lvs.coord.sand %>% 
  bind_cols(zoo.abnd.sand %>% select(station))
)

```

Make the plot and save it.  
```{r plot_lvm_sand}
(plot.lvm.sand <- ggplot(lvs.coord.sand) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("S", as.numeric((unique(lvs.coord.sand %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

```

```{r save_lvm_plot_sand}
## save the LVM plot for the sand stations
ggsave(file = here(figures.dir, "lvm_sand.png"), 
       plot.lvm.sand, 
       width = 15, units = "cm", dpi = 300)
```


##### **GLM fitting for abundance - environmental data**  
Let's fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.  
These functions all come from package **mvabund**.  
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (2009-2011 + 2013-2014) at each station, repeated for each replicate, and the sediment data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.       
```{r import_env_data_sand} 
env.sand <- read_csv(here(save.dir, "env_data_ordinations_sand.csv"))

## convert station to factor
(env.sand <- env.sand %>% 
    mutate(station = factor(station,
                            levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)
```
Station is a factor, the rest of the variables are numeric.  

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.  
```{r matrix_abnd_sand}
## there is already one subset of filtered count data (54 x 147) - use it 
zoo.mvabnd.sand <- mvabund(zoo.abnd.flt.sand)
```

###### **manyGLM by LVM clusters**
First, let's see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.  
```{r clusters_lvm_sand}
## construct the vector of the clusters by hand, it's easier that way.. 
lvm.clusters.sand <- c(rep(1, times = 18), rep(2:4, each = 9), rep(3, times = 9))

## convert to factor
(lvm.clusters.sand <- factor(lvm.clusters.sand))
```

Check the model assumptions. 
1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.  
Another way: direct plotting (variance ~ mean), for each species within each factor
level.  
```{r check_mean_variance_lvm_sand}
plot(manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.sand ~ lvm.clusters.sand, table = TRUE)
```

It's not perfect, but it's not too terrible either. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.
When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.
  
Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_sand}
glms.lvm.sand <- manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, 
                         family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_sand}
## residuals vs fitted values
plot(glms.lvm.sand)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.sand, which = 1:3)


# png(filename = here(figures.dir, "diag_pl_sand1.png"), width = 16, height = 10, units = "cm", res = 300)
# plot.manyglm(glms.lvm.sand, which = 2)
# dev.off()


### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
source(here(functions.dir, "default.plot.manyglm_grey.R"))
source(here(functions.dir, "plot.manyglm_grey.R"))

par(mfrow = c(2,2))
lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
par(mfrow = c(1, 1))

```

I really don't like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.  
Update (2019/05/02): while I still think these are fugly, I have no more time or nerves to deal with it. Rainbow shit it is.  
```{r save_diagn_plots_glms_lvm_sand}
png(here(figures.dir, "diagnostic_glms_lvm_sand.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(glms.lvm.sand, which = 1:3)
dev.off()
```

Save the model!  
```{r save_glms_lvm_sand}
write_rds(glms.lvm.sand, 
          here(save.dir, "glms_lvm_sand.RDS"))
```

Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_sand}
(glms.lvm.sand.summary <- summary(glms.lvm.sand, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)
```

The factor (here - groups outlined by the LVM) is highly significant according to the models.  
This also allows us to see which species exhibit a response to the chosen factor. 
The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. 
I'll save the summary for safekeeping, but I'll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).  
```{r save_summary_glms_lvm_sand}
write_rds(glms.lvm.sand.summary, 
          here(save.dir, "glms_lvm_sand_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_sand}
(glms.lvm.sand.aov <- anova.manyglm(glms.lvm.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
```
I probably shouldn't have printed all this out, but oh well who cares.  

Save the ANOVA, too.  
```{r save_anova_glms_lvm_sand}
write_rds(glms.lvm.sand.aov, 
          here(save.dir, "glms_lvm_sand_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern (here - clusters in the LVM, which are really the different soft-bottom habitats).  
```{r relative_taxon_contrib_glms_lvm_sand}
top_n_sp_glm <- function(glms.aov, tot.dev.expl = 0.75) {
  ## helper retrieving the top n species with the highest contribution to the patterns tested by the GLMs, in decreasing order.
  ## Arguments: glms.aov - results from an ANOVA on the fitted GLMs
  ##            dev.explained - proportion of explained deviance to use as cutoff
  
  ## get the change in deviance due to the tested pattern (= 2nd row from table of univariate test stats), and sort the species in order of decreasing contribution
  uni.sorted <- sort(glms.aov$uni.test[2, ], decreasing = TRUE, index.return = FALSE)

  ## start at 10 species and check how much of the deviance is explained by their contributions. Repeat, increasing by increments of 10 until the desired explained deviance (set at function call) is reached. 
  top.n.sp <- 10
  dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  
  while(dev.expl < tot.dev.expl) {
    top.n.sp <- top.n.sp + 10
    dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  }
  
  ## print the total deviance explained - just for information
  print(paste("Total deviance explained:", round(dev.expl, 3)))
  
  ## return the final top species (and their univariate contributions, just in case) 
  top.sp <- uni.sorted[1:top.n.sp]
  return(top.sp)
}

## get the top contributing species for the initial sand GLMs 
(top.sp.glms.lvm.sand <- top_n_sp_glm(glms.lvm.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.sand) <- names(top.sp.glms.lvm.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.sand
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_sand}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.lvm.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.sand))))
)

plot_top_n <- function(top.n.sp.data, mapping, labs.legend, lab.y, palette) {
  ## helper for plotting top n species. Was hoping to avoid repeating it from way back when, but no dice. 
  ## Arguments: top.n.sp.data - data frame (long) of top species' counts/biomasses at the different stations
  ##            mapping - mappings of the aesthetics
  ##            labs.legend - labels the use for the legend entries
  ##            lab.y - custom label for y axis
  ##            palette - custom colour palette (for consistency with other plots)
  
  ggplot(top.n.sp.data, mapping) +
    geom_point(alpha = 0.75) + # make points larger & partially transparent
    scale_color_brewer(palette = palette,  labels = labs.legend) + 
    ylab(lab.y) + 
    coord_flip() 
}


(plot.top.sp.glms.lvm.sand <- plot_top_n(abnd.top.sp.glms.lvm.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("S", as.numeric(unique(abnd.top.sp.glms.lvm.sand$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)
```

Well this is a nightmarish plot.. I'll probably just put this awfulness in a table and call it a day, or play with lvsplot and the modeled ordination plot, if a plot is what's needed.  

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is hopelessly ugly and clumsy (and I'll have to repeat it for the seagrass, too!), but I'm tired of being stuck on this. I still have many, MANY more things to do, and more time-consuming ones too..  
```{r table_relative_taxon_contrib_glms_lvm_sand}
top_sp_glms_table <- function(manyglms.obj.smry, group, p = 0.05) {
  ### extracts the top species in a group for which there is an observed effect in a manyglm test, at the specified probability level.
  ### Returns: tibble with the top species for the specified group/cluster, sorted (descending) by univariate LR value of the species, significant at the given p level. 
  
  ## extract the univariate LR coefficients of the species and their p-values 
  sp_univar <- as_tibble(manyglms.obj.smry$uni.test, rownames = "species")
  sp_p <- as_tibble(manyglms.obj.smry$uni.p, rownames = "species")

  ## combine in the same tibble
  sp_all <- left_join(sp_univar, sp_p, by = "species")  
  
  ## rename the columns
  sp_all <- sp_all %>% 
    rename_at(vars(contains(".x")), list(~str_replace_all(., pattern = ".x", ".LR"))) %>% 
    rename_at(vars(contains(".y")), list(~str_replace_all(., pattern = ".y", ".p")))
  
  ## filter only the group/cluster we want, at the p-level we want
  sp_all_flt <- sp_all %>% 
    select(species, contains(group)) %>% 
    filter_at(vars(contains(".p")), all_vars(. < p)) %>%
    arrange_at(vars(contains(".LR")), list(~desc(.)))

}

top.sp.abnd.glms.lvm.sand <- lapply(names(glms.lvm.sand.summary$aliased), function(x) top_sp_glms_table(glms.lvm.sand.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.sand2" etc.
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("lvm.clusters.sand")), list(~str_replace_all(., pattern = "lvm.clusters.sand", "group_"))))

top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.sand.long <- zoo.abnd.sand %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))

## sum sp abundances by group; nest by group
zoo.abnd.sand.long.smry <- zoo.abnd.sand.long %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, zoo.abnd.sand.long.smry %>% pull(group), ~left_join(.x, zoo.abnd.sand.long.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, c(18, 9, 18, 9), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

To determine the relative taxon contribution to patterns: LR statistic - a measure of strength of individual taxon contributions. LR expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or, compared to a critical value, to decide whether to reject the null model in favour of the alternative model.  

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.  
For **group 1** (= S1-S2), the species/taxa with significantly **higher abundance** are: Oligochaeta, H. filiformis, P. kefersteini, M. palmata, P. cirrifera, A. diadema (among others); and the ones with significantly **lower abundance** - even 0, in some cases - S. bidentata, B.lanceolatum, M. papillicornis, Melita palmata, P. jubatus, and so on.  
For **group 2** (= S3), the species with **higher abundance** are: B. lanceolatum, O. limacina, Oligochaeta (this is this strange artifact of 2013), P. kefersteini, L. flavocapitatus. The species with **lower abundance** are: H. filiformis, A. kagoshimensis, M. stammeri, Melinna palmata, etc.
For **group 3** (= S4-S6), the species with **higher abundance** are: C. gallina, L. mediterraneum - with very high dominance over practically all others; also Pseudocuma longicorne, Spio filicornis. The species with **lower abundance** are: H. filiformis, Oligochaetes (to a certain extent - they are still present, though), A. kagoshimensis, L. koreni, Harmothoe reticulata, Iphinoe tenella, Leiochone leiopygos.  
For **group 4** (= S5), the species with **higher abundance** are: Microdeutopus versiculatus, Eurydice dollfusi, Melita palmata, Polygordius neapolitanus, Polycirrus caliendrum, Polycirrus jubatus, Streptosyllis bidentata. The species with **lower abundance** are: A. kagoshimensis, Melinna palmata, P. cirrifera, P. ciliata, A. alba, I. tenella.   
I love how the species with the highest variances (e.g. C. gallina, the most conspicuous example) are consistently pushed back - have lower LR scores. This is very good - C. gallina in particular is dominant in group 3, but is present also in all other groups - its substrate/depth preferences are very wide, so this is not uncommon. It's not automatically pushed to the top of the list, but its reaction is detected by the manyGLM test. Neat! 
Contrast to the SIMPER results, where the species with the highest variance are consistently at the top - they contribute the most to the similarity, as per the test definition.  

I'm going to save these as separate files (manually), then format them as tables - I know it's a shame, but I'm too frustrated to figure out how to do it programmatically.  
I'll also put them in a word table in my final text, because I don't want to deal with a million separate ones (embedded excel tables don't split over multiple pages).  

**NB In my text, I'm switching the names/places of group 3 and 4, to be consistent with the SIMPER groups (I'm NOT going to repeat all this just to have the numbers match up). So the file names, table names, etc. remain as above. But in the text, I'll have the following: group 1 = S1-S2, group 2 = S3, group 3 = S5, group 4 = S4-S6. REMEMBER THIS SO THERE IS NO CONFUSION!**


###### **manyGLM by environmental parameters**  
Now, let's try to see a different thing - which environmental parameters best describe the species response.  
I'm going to use the PCA-filtered environmental data - it's still going to be a slog, with 7 potential predictors..  
First, construct the formula for the model - will do it separately in case I need to update it later, etc. This is the full formula with all explanatory variables.    
```{r formula_env_manyglm_full_sand}
(formula.env.glms.sand <- formula(paste("zoo.mvabnd.sand ~", 
                                        paste(env.sand %>% select(-station) %>% names(), collapse = "+")))
)
```

Fit the GLMs to the sand abundance data. 
```{r fit_glms_env_full_sand}
env.glms.sand <- manyglm(formula.env.glms.sand,
                         data = env.sand,
                         family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_env_full_sand}
## residuals vs fitted values
plot(env.glms.sand)


## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.sand, which = 1:3)


# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

```

Well, it's good enough if you ask me (still the kinda strange "line" at lin.pred = -6; otherwise residuals are random enough).  

Save the model!  
```{r save_glms_env_full_sand}
write_rds(env.glms.sand, 
          here(save.dir, "glms_env_sand.RDS"))
```


Before anything else, I want to try and reduce the model a little - to improve the fit/reduce run time.  
The automatic step functions that eliminate/add model terms sequentially don't work - they fail at the last step with a cryptic error about differing numbers of rows - I assume because manyglm has as left side term the whole community abundance matrix, and the functions don't really know how to deal with that. I don't understand enough about their internals to fix the problem, so I'm just going to write my own little automation based on the function drop1.  
```{r evaluate_glms_env_function}
evaluate_glms_env <- function(full.mod) {
  ### sequentially eliminate model terms in manyglms vs environmental parameters, and find the best model based on lowest AIC score.
  ### Arguments: full.mod - full model fit
  ### Returns: best manyglm model of environmental parameters; prints out the best model formula
  ### Dependencies: tidyverse   
  

  ## get the starting formula (= full model with all variables)
  start.formula <- formula(full.mod)

  drop_var <- function(mod) {
    ### helper picking the next variable to drop from a model to improve the fit (based on AIC)
    
    ## check the model AICs if variables are dropped one by one
    drop1.df <- as_tibble(drop1(mod), rownames = "drop_var") %>% arrange(AIC)
    
    ## pick the variable to drop next - the one resulting in the largest decrease in AIC
    drop.var <- drop1.df %>% filter(AIC == min(AIC)) %>% pull(drop_var)
    return(drop.var)
  }
  
  ## pick the variable to drop next
  drop.var <- drop_var(full.mod)

  if(drop.var != "<none>") {
     ## update the model formula, dropping the variable resulting in the largest decrease in AIC; then apply it to the model.
    new.formula <- update.formula(start.formula, paste0("~. -", drop.var))
    new.mod <- update(full.mod, new.formula)

    ## identify a new variable to drop that lowers the AIC
    drop.var <- drop_var(new.mod)
    
    ## repeat the steps above until the function can no longer find such a variable (i.e., dropping more variables doesn't improve the model fit)
    while(drop.var != "<none>") {
      new.formula <- update.formula(new.formula, paste0("~. -", drop.var))
      new.mod <- update(full.mod, new.formula)
      drop.var <- drop_var(new.mod)
    }
    
    ## print out the best model formula
    print(paste("Best model: ", paste(deparse(new.formula), collapse = "")))
    return(new.mod)
    
  } else {
    ## if the starting model is the best, print its formula (fat chance!)
    print(paste("Best model: ", paste(deparse(start.formula), collapse = "")))
    return(full.mod)
  }
  
}

```


Select the best reduced model of environmental variables for the sand stations.  
```{r select_top_glm_env_sand}
top.env.glm.red.sand <- evaluate_glms_env(env.glms.sand)

```

Check its fit. 
```{r explore_top_glm_env_red_sand}
## residuals vs fitted values
plot(top.env.glm.red.sand)

## all traditional (g)lm diagnostic plots
plot.manyglm(top.env.glm.red.sand, which = 1:3)
```

I think it's fine; might even be better than the full model.. 
Save it, too. 
```{r save_top_glm_env_red_sand}
write_rds(top.env.glm.red.sand, 
          here(save.dir, "glms_top_env_red_sand.RDS"))
```

Save the model diagnostic plots.  

```{r save_diagn_plots_top_glm_env_red_sand}
png(here(figures.dir, "diagnostic_top_glm_env_red_sand.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(top.env.glm.red.sand, which = 1:3)
dev.off()
```


Run ANOVA on this model.
```{r anova_top_glm_env_red_sand}
(top.env.glm.red.sand.aov <- anova.manyglm(top.env.glm.red.sand,
                                           test = "LR", p.uni = "adjusted",
                                           nBoot = 999, ## limit the number of permutations for a shorter run time   
                                           show.time = "all") 
)
```

So, it turns out that the long-term water column eutrophication (PO4, seston), the anthropogenic pressure in general (LUSI), and the sediment composition (gravel) explain the observed community patterns best. 

Save the ANOVA - I really, really don't want to have to repeat it.  
```{r save_anova_top_glm_env_red_sand}
write_rds(top.env.glm.red.sand.aov, 
          here(save.dir, "glms_top_env_red_sand_anova.RDS"))
```

Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).  
```{r relative_taxon_contrib_top_glm_env_red_sand}
## get the top contributing species for the environmental parameter sand GLMs 
(top.sp.glms.env.red.sand <- top_n_sp_glm(top.env.glm.red.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   DON'T BE IN A HURRY TO DO THAT IF YOU WANT TO SUBSET THE ORIGINAL MATRIX BEFORE RUNNING TRAITGLM 
names(top.sp.glms.env.red.sand) <- names(top.sp.glms.env.red.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

```

I'm going to plot these top contributing species, but I'm not using the plot. At least this time it's more manageable, but still not presentable enough.. 

```{r plot_relative_taxon_contrib_top_glm_env_red_sand}
## get the species and their abundances from the original count data, and transform them to long format
abnd.top.sp.glms.env.red.sand <- zoo.abnd.sand %>% 
  select(station, names(top.sp.glms.env.red.sand)) %>% 
  gather(key = "species", value = "count", -station) %>% 
  ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
  mutate(species = factor(species, levels = rev(names(top.sp.glms.env.red.sand)))) %>% 
  ## add clusters from LVM as a column
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1,
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))



## add the significant environmental parameters from the model
(abnd.top.sp.glms.env.red.sand <- left_join(abnd.top.sp.glms.env.red.sand, 
                                            env.sand %>% select(station, PO4, seston, LUSI, gravel), 
                                            by = "station") 
    
)


(plot.top.sp.glms.env.red.sand <- plot_top_n(abnd.top.sp.glms.env.red.sand,
                                             mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                             labs.legend = unique(abnd.top.sp.glms.env.red.sand$group),
                                             lab.y = "Abundance (log(y/min + 1))",
                                             palette = "Set2") + 
    theme(legend.position = "top")
)
```

FIXME>>>
Try another thing - manually, unfortunately: this same nightmare, but colored by the values of each model term. 
```{r composite_plot_relative_taxon_contrib_top_glm_env_sand}
ggplot(abnd.top.sp.glms.env.red.sand,
       mapping = aes(x = species, y = log_y_min(count), colour = seston)) + 
  geom_point() + 
  coord_flip()
```



Extract the taxon information (univariate tests) from the model ANOVA to present as a table (probably better than this plot, although it's informative).  
```{r table_relative_taxon_contrib_top_glm_env_red_sand}
## extract the univariate test coefficients (LR) from the environmental model ANOVA. NB keep the row names when converting the matrix to tibble! 
table.top.sp.glms.env.red.sand <- as_tibble(top.env.glm.red.sand.aov$uni.test, rownames = "var")

## fix the species names - remove first dot  
names(table.top.sp.glms.env.red.sand) <- names(table.top.sp.glms.env.red.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

## subset only the top species (explaining ~75% of the dataset variation)
table.top.sp.glms.env.red.sand <- table.top.sp.glms.env.red.sand %>% 
  select(var, names(top.sp.glms.env.red.sand))

## transpose, because a table with 50 columns is just unreadable
(table.top.sp.glms.env.red.sand <- table.top.sp.glms.env.red.sand %>%
    gather(key = species, value = value, -var) %>% 
    spread(key = var, value = value) %>% 
    ## arrange as before (terms in the order they appear in the model, and by descending value of the LR for the first model term - here, PO4). Also get rid of the intercept (it's all-NA anyway).
    select(species, PO4, seston, LUSI, gravel) %>%
    arrange(desc(PO4)) 
)
```

Save this to a file - will have to format it as a nice table by hand, unfortunately. 
```{r save_table_relative_taxon_contrib_top_glm_env_red_sand}
write_csv(table.top.sp.glms.env.red.sand, 
          here(save.dir, "taxa_contrib_glms_top_env_red_sand.csv"))
```


Calculate the percentage contribution of each of these species to each of the model terms (Dev(term) = Sum-of-LR - sum of the LRs for the individual univariate species tests).. 
```{r table_prop_relative_taxon_contrib_top_glm_env_red_sand}
## get the total deviance (Sum-of-LR) for each model term
(dev.terms.top.glms.env.sand <- as_tibble(top.env.glm.red.sand.aov$table, rownames = "var") %>%
   ## get rid of unnecessary variables (I only want the deviance value for each term) and intercept term 
   select(var, Dev) %>% 
   filter(var != "(Intercept)") %>% 
   ## transpose 
   gather(variable, value, -var) %>%
   spread(var, value) %>% 
   ## get rid of first column and rearrange columns to match table of deviances of univariate tests for species 
   select(-variable) %>% 
   select(PO4, seston, LUSI, gravel)
)  

## calculate the proportion contribution of each species to each parameter deviance
prop.top.sp.glms.env.red.sand <- map2_df(table.top.sp.glms.env.red.sand %>% select(-species),
                                         dev.terms.top.glms.env.sand, 
                                         ~.x/.y)

## add back the species 
(prop.top.sp.glms.env.red.sand <- bind_cols(table.top.sp.glms.env.red.sand %>% select(species), 
                                            prop.top.sp.glms.env.red.sand)
)

```


Final analysis to try: which species respond differently to different environmental parameters?
(= traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix).  
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.   
```{r sp_response_top_glm_env_red_sand}
sp.response.glms.env.red.sand <- traitglm(L = mvabund(zoo.abnd.flt.sand[, names(top.sp.glms.env.red.sand)]), 
                                          R = as.matrix(env.sand %>% select(PO4, seston, LUSI, gravel)), 
                                          method = "manyglm")


sp.response.glms.env.red.sand$fourth.corner


# plot this 
a <- max(abs(sp.response.glms.env.red.sand$fourth.corner))
colort <- colorRampPalette(c("blue","white","red")) 
plot.spp <- lattice::levelplot(t(as.matrix(sp.response.glms.env.red.sand$fourth.corner)), xlab = "Environmental Variables",
                     ylab = "Species", col.regions = colort(100), at = seq(-a, a, length = 100),
                     scales = list(x = list(rot = 45)))
print(plot.spp)
```

When using LASSO (method = "glm1path"), the algorithm fails to converge - I'm not sure how to interpret it.. Maybe because the function tests each individual species:env.parameter interaction (does it really??), and none of them by themselves are sufficient to explain a species' response. Not to mention the fact that the samples are not really independent (they are replicates at 6 sites, repeated 3 times).  
When using method = "manyglm", the result is the one shown above. It's still a bitch to interpret - for example, what is the interpretation of an increase in abundance with for ex. high PO4, but low LUSI? Where are these conditions ever met?   

In fact, everything points towards the conclusion that a species response is determined by a combination of eutrophication parameters in its environment (water column characteristics), and the composition of the sediments (organic matter and granulometry).  

This is actually sort of similar to the PERMANOVA results, in this particular case. However, it's much more parsimonious.  
In the future, I'm leaning more towards the modeling approach - it allows you to check the model fit to one's real data; also, there are no data reductions due to calculation of distance matrices.  



#### **Seagrass stations (Burgas Bay, 2013-2014)**  
Import zoobenthic abundance data (cleaned and prepared).  
```{r import_zoo_abnd_zostera}
zoo.abnd.zostera <- read_csv(here(save.dir, "abnd_zostera_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.zostera <- zoo.abnd.zostera %>% 
    mutate(station = factor(station, levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)
```

Remove the all-0 species (= not present in the current dataset).  
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it's unlikely they carry important information, but it would probably improve the run times).  
```{r filter_zoo_data_zostera}
(zoo.abnd.flt.zostera <- zoo.abnd.zostera %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
```


##### **LVM - model-based ordination**
Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.   
I'm including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of **species composition**.   
NB this takes about a million years to run! 
```{r lvm_zostera}
lvm.zostera <- boral(y = zoo.abnd.flt.zostera, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:5, times = c(8, 8, 4, 8, 4)), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

```

Check the summary and diagnostic plots for the LVM.  
```{r summary_lvm_zostera}
summary(lvm.zostera)

## model fit diagnostic plots
plot(lvm.zostera) 
```
The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a (more or less) normal distribution of the residuals) - the model fits the data pretty well.  

Save the zostera LVM.  
```{r save_lvm_zostera}
write_rds(lvm.zostera, 
          here(save.dir, "lvm_zostera.RDS"))
```

Save the diagnostic plots.  
```{r save_diagn_plots_lvm_zostera}
png(here(figures.dir, "diagnostic_lvm_zostera.png"), width = 25, height = 20, units = "cm", res = 300)
par(mfrow = c(2, 2))
plot(lvm.zostera)
par(mfrow = c(1, 1))
dev.off()
```


Examine the biplot obtained by fitting the LVM, as well as the 20 most "important" species.   
```{r check_biplot_lvm_zostera}
lvsplot(lvm.zostera, jitter = T, biplot = TRUE, ind.spp = 20)
```

All in all, the final result resembles the nMDS ordination very much - same stretched clusters (Poda + Otmanli, Vromos pretty much apart, Gradina +- Ropotamo). I don't see much difference with the nMDS. 
The main difference seems to be the distance between the 2 years for Poda ana Otmanli - the LVM enlarges it. Have to remember to test for year effect! 
The run time is actually not that bad for the seagrasses.
The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I'm not adding the species on top, first because I'm too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.   
```{r extract_lvm_coord_zostera}
## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.zostera <- as_tibble(lvm.zostera$lv.median)

## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.zostera <- lvs.coord.zostera %>% 
  bind_cols(zoo.abnd.zostera %>% select(station))
)

```

Make the plot and save it.  
```{r plot_lvm_zostera}
(plot.lvm.zostera <- ggplot(lvs.coord.zostera) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("Z", as.numeric((unique(lvs.coord.zostera %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

```

Well, this is a weird one - this plot is flipped around 0 compared to the one that boral's plotting function gives. Otherwise nothing changes - the spatial relationships between samples are preserved. I suppose it doesn't matter much - the axes are arbitrary after all, but strange that it happens.  

```{r save_plot_lvm_zostera}
## save the LVM plot for the seagrass
ggsave(file = here(figures.dir, "lvm_zostera.png"), 
       plot.lvm.zostera, 
       width = 15, height = 10, units = "cm", dpi = 300)
```

##### **GLM fitting for abundance - environmental data**  
Fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.  
These functions all come from package **mvabund**.  
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (as long-term as available, at least) at each station, repeated for each replicate, the sediment data (2013-2014), and the seagrass data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.       
```{r import_env_data_zostera} 
env.zostera <- read_csv(here(save.dir, "env_data_ordinations_zostera.csv"))

## convert station to factor
(env.zostera <- env.zostera %>% 
    mutate(station = factor(station,
                            levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)
```
Station is a factor, the rest of the variables are numeric.  

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.  
```{r matrix_abnd_zostera}
## there is already one subset of filtered count data (32 x 94) - use it 
zoo.mvabnd.zostera <- mvabund(zoo.abnd.flt.zostera)
```

###### **manyGLM by LVM clusters**
First, let's see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.  
I'm going to try something new here - 1) loose clusters from the LVM ordination, 1 = Poda-Otmanli, 2 = Vromos, 3 = Gradina-Ropotamo. 2) stations as clusters, as I did before for the seagrass data, although I don't believe it's valid/justified to do so... 3) another possible configuration of clusters from the LVM ordination: 1 = Z1-Z2, 2 = Z3, 3 = Z4, 4 = Z5.   
```{r clusters_lvm_zostera}
## construct the vectors of the clusters by hand - first, situation 1 above
lvm.clusters.zostera.1 <- rep(1:3, times = c(16, 4, 12))
(lvm.clusters.zostera.1 <- factor(lvm.clusters.zostera.1))

## again, for case 2
lvm.clusters.zostera.2 <- rep(1:5, times = c(8, 8, 4, 8, 4))
(lvm.clusters.zostera.2 <- factor(lvm.clusters.zostera.2))

## again, for case 3
lvm.clusters.zostera.3 <- rep(1:4, times = c(16, 4, 8, 4))
(lvm.clusters.zostera.3 <- factor(lvm.clusters.zostera.3))
```

**LVM clusters - case 1**
Check the model assumptions. 
1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.  
Another way: direct plotting (variance ~ mean), for each species within each factor
level.  
```{r check_mean_variance_lvm_zostera_1}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, table = TRUE)
```

It's not perfect, but it's not too terrible either. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.
When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.
  
Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_1}
glms.lvm.zostera.1 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_1}
## residuals vs fitted values
plot(glms.lvm.zostera.1)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.1, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

```

I really don't like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.  
Save the model!  
```{r save_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1, 
          here(save.dir, "glms_lvm_zostera_1.RDS"))
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_1}
(glms.lvm.zostera.1.summary <- summary(glms.lvm.zostera.1, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)
```

The factor is highly significant according to the models.  
This also allows us to see which species exhibit a response to the chosen factor. 
The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. 
I'll save the summary for safekeeping, but I'll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).  
```{r save_summary_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1.summary, 
          here(save.dir, "glms_lvm_zostera_1_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_1}
(glms.lvm.zostera.1.aov <- anova.manyglm(glms.lvm.zostera.1, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time
                                    pairwise.comp = ~lvm.clusters.zostera.1, ## check the pairwise comparison between clusters
                                    show.time = "all") 
)
```

Aaaand the differences between clusters are highly significant in this iteration.. 

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1.aov, 
          here(save.dir, "glms_lvm_zostera_1_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_1}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.1 <- top_n_sp_glm(glms.lvm.zostera.1.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.1) <- names(top.sp.glms.lvm.zostera.1) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.1
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_1}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.1 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.1)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.1)))) %>% 
   mutate(group = factor(case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                                   station == "Vromos" ~ 2, 
                                   station %in% c("Gradina", "Ropotamo") ~ 3))) ## add the groups to the long df 
)


(plot.top.sp.glms.lvm.zostera.1 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.1,
                                         mapping = aes(x = species, y = log_y_min(count), colour = group),
                                         labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.1$group))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())

)
```

Well this is a nightmarish plot, but more tolerable than the one for the sand stations - there are less species here, so at least it's readable..   

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_1}
top.sp.abnd.glms.lvm.zostera.1 <- lapply(names(glms.lvm.zostera.1.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.1.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.1")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.1", "group_"))))

top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.1 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                           station == "Vromos" ~ 2, 
                           station %in% c("Gradina", "Ropotamo") ~ 3)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.1.smry <- zoo.abnd.zostera.long.1 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, zoo.abnd.zostera.long.1.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.1.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, c(16, 4, 12), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.  
I have to say, in the case of the seagrasses and case 1 clusters, there are much fewer species that exhibit a significant response - around 10 for each group.     
The LRs are lower for groups 2 and 3 - not sure if this means anything, but for group 1 they are much much higher..   
For **group 1** (= Z1-Z2), the species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Oligochaeta, H. filiformis, Polydora ciliata, Prionospio cirrifera, R. membranacea, A. alba, A.diadema, M. acherusicum; and the only one with a significantly **lower abundance** - Chamelea gallina.   
For **group 2** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A.dadema. The species with **lower abundance** are: B. reticulatum, A. alba, Oligochaeta, S. clavata, P. ciliata, P. cirrifera, H. filiformis.  
For **group 3** (= Z4-Z5), the species with **higher abundance** are: Cumella limicola, Apseudopsis ostroumovi, Capitella capitata, Mytilaster lineatus, Loripes orbiculatus; less so, but still present - C. gallina, S. clavata. The species with **lower abundance** are: Abra alba, Melinna palmata (totally absent).  


I'll test each station as its own group, too (as I did before, with the classical multivariate methods) - I'm not sure how much I can trust this grouping (in particular group 3 is a bit far-fetched, if you ask me..).  


**LVM clusters - case 2**
Check the model assumptions.  
```{r check_mean_variance_lvm_zostera_2}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, table = TRUE)
```

It's not perfect, but it's not too terrible either. I think it's a little worse than the case 1 fit.  

2. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_2}
glms.lvm.zostera.2 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_2}
## residuals vs fitted values
plot(glms.lvm.zostera.2)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.2, which = 1:3)
```

Save the model!  
```{r save_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2, 
          here(save.dir, "glms_lvm_zostera_2.RDS"))
```

Save the model diagnostic plots - only for this one, since - spoiler alert! - I'm going with it in the end; it's marginally better than the other two options.   
```{r save_diagn_plots_glms_lvm_zostera_2}
png(here(figures.dir, "diagnostic_glms_lvm_zostera_2.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(glms.lvm.zostera.2, which = 1:3)
dev.off()
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_2}
(glms.lvm.zostera.2.summary <- summary(glms.lvm.zostera.2, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
```

The factor is highly significant according to the models.  
 
Again, save the summary for safekeeping, but also run an anova.  
```{r save_summary_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2.summary, 
          here(save.dir, "glms_lvm_zostera_2_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_2}
(glms.lvm.zostera.2.aov <- anova.manyglm(glms.lvm.zostera.2, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         pairwise.comp = ~lvm.clusters.zostera.2, ## check the pairwise comparison between clusters
                                         show.time = "all") 
)
```

Again, these groups are sufficiently different from one another.. No clue here. 

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2.aov, 
          here(save.dir, "glms_lvm_zostera_2_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_2}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.2 <- top_n_sp_glm(glms.lvm.zostera.2.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.2) <- names(top.sp.glms.lvm.zostera.2) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.2
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_2}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.2 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.2)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.2)))) %>% 
   mutate(group = factor(case_when(station == "Poda" ~ 1,
                                   station == "Otmanli" ~ 2,
                                   station == "Vromos" ~ 3, 
                                   station == "Gradina" ~ 4, 
                                   station == "Ropotamo" ~ 5)))
)


(plot.top.sp.glms.lvm.zostera.2 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.2,
                                              mapping = aes(x = species, y = log_y_min(count), colour = group),
                                              labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.2$group))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())

)
```


Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_2}
top.sp.abnd.glms.lvm.zostera.2 <- lapply(names(glms.lvm.zostera.2.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.2.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.2")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.2", "group_"))))

top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.2 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station == "Poda" ~ 1,
                           station == "Otmanli" ~ 2, 
                           station == "Vromos" ~ 3, 
                           station == "Gradina" ~ 4, 
                           station == "Ropotamo" ~ 5)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.2.smry <- zoo.abnd.zostera.long.2 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, zoo.abnd.zostera.long.2.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.2.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, c(8, 8, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In the case of the seagrasses and case 2 clusters (= stations), the picture is still more unclear.. I suppose this is in no small part because of the differences 2013-14 - very marked for Poda and Otmanli. I suspect the stations changed in these two years (we were looking for Z. noltii in 2014 in particular) - but still, there is much variability. In the future, it's probably going to be worth it to have more stations in a meadow, if we really want to have an idea of the communities there, and their variability.  
The LRs seem to be a bit lower for groups 2, 4, maybe 5 too - still not sure if you can use that as a significance measure.  
For now, in **group 1** (= Z1), it's hard to pick some characteristic species - because of the variability between 2013-2014, no doubt. The species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Polydora ciliata, Prionosprio cirrifera (+ others, medium abundance); and the ones with a significantly **lower abundance** - or even absent - C. gallina, A. ostroumovi, S. clavata, C. limicola, C. costulata, S. hystrix, S. gracilis, T. pullus.   
For **group 2** (= Z2), the species with **higher abundance** - which is not really all that high; this group is also loose, hard to distinguish from group 1 - are: S. gracilis, M. lineatus, P. ciliata. The only species with **lower abundance** - in fact 0 - is Alitta succinea.  
For **group 3** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A. diadema. The species with **lower abundance** (or 0) are: B. reticulatum, P. ciliata, P. cirrifera, A. alba, A. succinea, S. clavata, Oligochaeta, A. improvisus.  
For **group 4** (= Z4), the species with **higher abundance** are: M. lineatus (very much so); C. limicola, P. kefersteini, C. gallina, C. capitata. The species with **lower abundance** (or 0) are: P. ciliata, P. cirrifera, A. succinea, A. improvisus, A. alba.  
For **group 5** (= Z5), the species with **higher abundance** are: A. ostroumovi, C. capitata, Oligochaeta. The species with **lower abundance** (or 0) are: R. splendida, T. pullus.  


**LVM clusters - case 3**
Last try: group 1 = Z1-Z2, group 2 = Z3, group 3 = Z4, group 4 = Z5.  
Check the model assumptions.  
```{r check_mean_variance_lvm_zostera_3}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, table = TRUE)
```

More or less the same as case 2 before it. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_3}
glms.lvm.zostera.3 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_3}
## residuals vs fitted values
plot(glms.lvm.zostera.3)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.3, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(3,3))
# lapply(3:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(3, 3))

```

Save the model!  
```{r save_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3, 
          here(save.dir, "glms_lvm_zostera_3.RDS"))
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_3}
(glms.lvm.zostera.3.summary <- summary(glms.lvm.zostera.3, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
```

The factor is highly significant according to the models.  
 
Again, save the summary for safekeeping, but also run an anova.  
```{r save_summary_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3.summary, 
          here(save.dir, "glms_lvm_zostera_3_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_3}
(glms.lvm.zostera.3.aov <- anova.manyglm(glms.lvm.zostera.3, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         pairwise.comp = ~lvm.clusters.zostera.3, ## check the pairwise comparisons between clusters
                                         show.time = "all") 
)
```

According to the pairwise comparison, the case 3 clusters are significantly different from one another.. apparently sufficiently so.  

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3.aov, 
          here(save.dir, "glms_lvm_zostera_3_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_3}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.3 <- top_n_sp_glm(glms.lvm.zostera.3.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.3) <- names(top.sp.glms.lvm.zostera.3) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.3
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_3}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.3 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.3)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.3)))) %>% 
   mutate(group = factor(case_when(station %in% c("Poda", "Otmanli") ~ 1,
                                   station == "Vromos" ~ 2, 
                                   station == "Gradina" ~ 3, 
                                   station == "Ropotamo" ~ 4)) ## add the groups
          )
)

(plot.top.sp.glms.lvm.zostera.3 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.3,
                                              mapping = aes(x = species, y = log_y_min(count), colour = group),
                                              labs.legend = paste0("group", as.character(levels(abnd.top.sp.glms.lvm.zostera.3$group))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top", legend.title = element_blank())

)
```


Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_3}
top.sp.abnd.glms.lvm.zostera.3 <- lapply(names(glms.lvm.zostera.3.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.3.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera3" etc.
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.3")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.3", "group_"))))

top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.3 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1,
                           station == "Vromos" ~ 2, 
                           station == "Gradina" ~ 3, 
                           station == "Ropotamo" ~ 4)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.3.smry <- zoo.abnd.zostera.long.3 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, zoo.abnd.zostera.long.3.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.3.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, c(16, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In the case of the seagrasses and case 3 clusters, the picture is still more confusing..  
The LRs seem to be a bit lower for groups 2 and 3, maybe 4 too - still not sure if you can use that as a significance measure.  
For now, in **group 1** (= Z1-Z2), the species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Oligochaeta, Heteromastus filiformis, Polydora ciliata, Prionosprio cirrifera, Rissoa membranacea, Abra alba, Ampelisca diadema (+ others, medium abundance); and the ones with a significantly **lower abundance** - or even absent -  S. clavata,  A. ostroumovi, C. gallina, T. pullus.   
There are more species singled out for this cluster, probably because of the variability between the two years of sampling.  
For **group 2** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A. diadema. The species with **lower abundance** - in fact 0 - are B. reticulatum, P. cirrifera, S. clavata, A. alba, P. ciliata, oligochaetes, H. filiformis, R. splendida.  
For **group 3** (= Z4), the species with **higher abundance** are: M. lineatus, less so - C. limicola, L. orbiculatus, P. kefersteini, C. capitata, etc. The species with **lower abundance** (or 0) are: P. cirrifera, P. ciliata, A. alba, etc.  
For **group 4** (= Z5), the species with **higher abundance** are: A. ostoumovi, C. capitata, oligochaetes (very abundant, but with a small LR - nice!). The species with **lower abundance** (or 0) are: R. splendida, S. clavata, C. limicola.  


**All in all, I think that group 1 (Poda + Otmanli) holds, and so does group 2 (Vromos). The question is whether to separate Gradina and Ropotamo into 2 groups, or if they make more sense together. Ropotamo is characterized by a very high number of oligochaetes, while Gradina's most distinguishing characteristic is the high number of M. lineatus - mostly very small ones, attached to the rhizomes, close to the sediment surface I presume. Both stations have C. limicola in medium abundance, a species that is not present anywhere else (is it?).** 


Try to compare the three models.. 
```{r compare_glms_lvm_zostera_1}
(glms.lvm.zostera.comp <- anova(glms.lvm.zostera.1,
                                glms.lvm.zostera.2, 
                                glms.lvm.zostera.3, 
                                p.uni = "adjusted")
)

```

Well this is tough to interpret.. Multivariate test table's Dev is decrement from upper model, so each p-value indicates the difference between the model and upper one is statistically significant... But no info on which model represents the species matrix best.  

I'll go with the model with the lowest AIC, since there is no other objective criterion to go with.. This happens to be model 2 (groups = stations). Exactly the same result as from the classical methods.  
```{r compare_glms_lvm_zostera_2}
glms.lvm.zostera.1$AICsum
glms.lvm.zostera.2$AICsum
glms.lvm.zostera.3$AICsum
```


###### **manyGLM by environmental parameters**  
Now, let's try to see a different thing - which environmental parameters best describe the species response.  
I'm going to use the PCA-filtered environmental data - it's still going to be a slog, with 7 potential predictors..  
First, construct the formula for the model - will do it separately in case I need to update it later, etc.  
NB there is year here - I want to try with it first!! And I don't want the Secchi depth - it has NAs for Vromos.  
```{r formula_env_manyglm_full_zostera}
(formula.env.glms.zostera <- formula(paste("zoo.mvabnd.zostera ~",
                                           paste(env.zostera %>% select(-c(station, secchi)) %>% names(), collapse = "+")))
)
```

Fit the GLMs - including all environmental parameters - to the zostera abundance data. 
```{r fit_glms_env_full_zostera}
env.glms.zostera <- manyglm(formula.env.glms.zostera,
                            data = env.zostera,
                            family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_env_full_zostera}
## residuals vs fitted values
plot(env.glms.zostera)


## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.zostera, which = 1:3)


# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

```

Well, it's good enough if you ask me (still the kinda strange "line" at lin.pred = -6; otherwise residuals are random enough).  

Save the model!  
```{r save_glms_env_full_zostera}
write_rds(env.glms.zostera, 
          here(save.dir, "glms_env_zostera.RDS"))
```

Before going off and running an ANOVA to check which predictors best explain the species abundance patterns, I'll try to reduce the model a little - it might even improve the fit, not to mention the run time.  
```{r select_top_glm_env_zostera}
## selection function defined in the sand section 
top.env.glm.red.zostera <- evaluate_glms_env(env.glms.zostera)

```

Check its fit. 
```{r explore_top_glm_env_red_zostera}
## residuals vs fitted values
plot(top.env.glm.red.zostera)


## all traditional (g)lm diagnostic plots
plot.manyglm(top.env.glm.red.zostera, which = 1:3)
```

I think it's fine; might even be better than the full model.. 
Save it, too. 
```{r save_top_glm_env_red_zostera}
write_rds(top.env.glm.red.zostera, 
          here(save.dir, "glms_top_env_red_zostera.RDS"))
```

Save the diagnostic plots.  
```{r save_diagn_plots_top_glm_env_red_zostera}
png(here(figures.dir, "diagnostic_top_glm_env_red_zostera.png"), width = 25, height = 20, units = "cm", res = 300)
plot.manyglm(top.env.glm.red.zostera, which = 1:3)
dev.off()
```

Run ANOVA on this model.
```{r anova_top_glm_env_red_zostera}
(top.env.glm.red.zostera.aov <- anova.manyglm(top.env.glm.red.zostera,
                                              test = "LR", p.uni = "adjusted", 
                                              nBoot = 999, ## limit the number of permutations for a shorter run time   
                                              show.time = "all") 
)
```

Nice, all terms are significant now! 
Again, as with the sand samples, there is one eutrophication term + one sediment composition + seagrass parameters. Seems reasonable enough.  

Save this ANOVA (takes too long to run anew).  
```{r save_anova_top_glm_env_red_zostera}
write_rds(top.env.glm.red.zostera.aov, 
          here(save.dir, "glms_top_env_red_zostera_anova.RDS"))
```


Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).  
```{r relative_taxon_contrib_top_glm_env_red_zostera}
## get the top contributing species for the environmental parameter zostera GLMs 
(top.sp.glms.env.red.zostera <- top_n_sp_glm(top.env.glm.red.zostera.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   DON'T BE IN A HURRY TO DO THAT IF YOU WANT TO SUBSET THE ORIGINAL MATRIX BEFORE RUNNING TRAITGLM 
names(top.sp.glms.env.red.zostera) <- names(top.sp.glms.env.red.zostera) %>% 
  str_replace(pattern = "\\.", replacement = " ")

```

I'm going to plot these top contributing species, but I'm not using the plot. At least this time it's more manageable, but still not presentable enough.. 

```{r plot_relative_taxon_contrib_top_glm_env_red_zostera}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.env.red.zostera <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.env.red.zostera)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.env.red.zostera)))) %>% 
   ## add clusters from LVM as a column
   mutate(group = case_when(station == "Poda" ~ 1, 
                            station == "Otmanli" ~ 2, 
                            station == "Vromos" ~ 3, 
                            station == "Gradina" ~ 4, 
                            station == "Ropotamo" ~ 5))
)


(plot.top.sp.glms.env.red.zostera <- plot_top_n(abnd.top.sp.glms.env.red.zostera,
                                         mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                         labs.legend = unique(abnd.top.sp.glms.env.red.zostera$group),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) + 
    theme(legend.position = "top")

)
```


Extract the taxon information (univariate tests) from the model ANOVA to present as a table (probably better than this plot, although it's informative).  
```{r table_relative_taxon_contrib_top_glm_env_red_zostera}
## extract the univariate test coefficients (LR) from the environmental model ANOVA. NB keep the row names when converting the matrix to tibble! 
table.top.sp.glms.env.red.zostera <- as_tibble(top.env.glm.red.zostera.aov$uni.test, rownames = "var")

## fix the species names - remove first dor  
names(table.top.sp.glms.env.red.zostera) <- names(table.top.sp.glms.env.red.zostera) %>% 
  str_replace(pattern = "\\.", replacement = " ")

## subset only the top species (explaining ~75% of the dataset variation)
table.top.sp.glms.env.red.zostera <- table.top.sp.glms.env.red.zostera %>% 
  select(var, names(top.sp.glms.env.red.zostera))

## transpose, because a table with 50 columns is just unreadable
(table.top.sp.glms.env.red.zostera <- table.top.sp.glms.env.red.zostera %>%
    gather(key = species, value = value, -var) %>% 
    spread(key = var, value = value) %>% 
    ## arrange as before (terms in the order they appear in the model, and by descending value of the LR for the first model term - here, Ntotal). Also get rid of the intercept (it's all-NA anyway).
    select(species, Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet) %>%
    arrange(desc(Ntotal)) 
)
```

Save this to a file - will have to format it as a nice table by hand, unfortunately. 
```{r save_table_relative_taxon_contrib_top_glm_env_red_zostera}
write_csv(table.top.sp.glms.env.red.zostera, 
          here(save.dir, "taxa_contrib_glms_top_env_red_zostera.csv"))
```


Calculate the percentage contribution of each of these species to each of the model terms (Dev(term) = Sum-of-LR - sum of the LRs for the individual univariate species tests).. 
```{r table_prop_relative_taxon_contrib_top_glm_env_red_zostera}
## get the total deviance (Sum-of-LR) for each model term
(dev.terms.top.glms.env.zostera <- as_tibble(top.env.glm.red.zostera.aov$table, rownames = "var") %>%
   ## get rid of unnecessary variables (I only want the deviance value for each term) and intercept term 
   select(var, Dev) %>% 
   filter(var != "(Intercept)") %>% 
   ## transpose 
   gather(variable, value, -var) %>%
   spread(var, value) %>% 
   ## get rid of first column and rearrange columns to match table of deviances of univariate tests for species 
   select(-variable) %>% 
   select(Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet)
)  

## calculate the proportion contribution of each species to each parameter deviance
prop.top.sp.glms.env.red.zostera <- map2_df(table.top.sp.glms.env.red.zostera %>% select(-species), 
                                            dev.terms.top.glms.env.zostera,
                                            ~.x/.y)

## add back the species 
(prop.top.sp.glms.env.red.zostera <- bind_cols(table.top.sp.glms.env.red.zostera %>% select(species), 
                                               prop.top.sp.glms.env.red.zostera)
)
```




I'll do the pseudo-traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix), although I don't think it will amount to anything useful.   
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.   
```{r sp_response_top_glm_env_red_zostera}
sp.response.glms.env.red.zostera <- traitglm(L = mvabund(zoo.abnd.flt.zostera[, names(top.sp.glms.env.red.zostera)]), 
                                             R = as.matrix(env.zostera %>% select(Ntotal, sand, shoot_count, ag_biomass_wet, bg_biomass_wet)), 
                                             method = "manyglm")


sp.response.glms.env.red.zostera$fourth.corner


# plot this 
a.z <- max(abs(sp.response.glms.env.red.zostera$fourth.corner))
colort <- colorRampPalette(c("blue","white","red")) 
plot.spp.z <- lattice::levelplot(t(as.matrix(sp.response.glms.env.red.zostera$fourth.corner)), xlab = "Environmental Variables",
                     ylab = "Species", col.regions = colort(100), at = seq(-a.z, a.z, length = 100),
                     scales = list(x = list(rot = 45)))
print(plot.spp.z)
```

Here at least the directions are a little more coherent than the environmental parameters for the sand stations (seagrass biomasses more or less in the same direction, etc.). The below-ground biomass exerts more pronounced influence on the specific abundances - normal, since most of these are infauna.  

